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College Mathematics for Business Economics Life Sciences and Social Sciences 12th edition Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen - Solutions
In Problem, find fʹ(x) and simplify. f(x) = 6e-2x
In Problem, find fʹ(x) and simplify. f(x) = ex2+3x+1
In Problem, find fʹ(x) and simplify. f(x) = (4x + 3)1/2
In Problem, find fʹ(x) and simplify.f(x) = (x5 + 2)-3
In Problem, find fʹ(x) and simplify. f(x) = 2 ln(x2 - 3x + 4)
In Problem, find fʹ(x) and simplify. f(x) = (x - 2 ln x)4
In Problem, find f'(x) and the equation of the line tangent to the graph off at the indicated value of x. Find the value(s) of x where the tangent line is horizontal. f(x) = (3x - 1)4 ; x = 2
In Problem, find f'(x) and the equation of the line tangent to the graph off at the indicated value of x. Find the value(s) of x where the tangent line is horizontal. f(x) = (x + 8x)1/2; x = 4
In Problem, find f'(x) and the equation of the line tangent to the graph off at the indicated value of x. Find the value(s) of x where the tangent line is horizontal. f(x) = ln(l - x2 + 2x4); x = 1
In Problem find the indicated derivative and simplify
In Problem find the indicated derivative and simplify
In Problem find the indicated derivative and simplify
In Problem find the indicated derivative and simplify
In Problem, find the indicated derivative and simplify. G'(t) if G(t) = (1 - e2t)2
In Problem find the indicated derivative and simplify y' if y = [ln(x2 + 3)]3/2
In Problem find the indicated derivative and simplify.
In Problem, find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x. f (x) = x2(1 - x )4; x = 2
In Problem, find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.
In Problem, find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.
In Problem, find fʹ(x) and find the value (s) of x where the tangent line is horizontal. f(x) = x3 (x - 7 )4
In Problem, find fʹ(x) and find the value (s) of x where the tangent line is horizontal.
In Problem, find fʹ(x) and find the value (s) of x where the tangent line is horizontal. f (x) = √x2 + 4x +5
In Problem, find each derivative and simplify.
In Problem, find each derivative and simplify.
In Problem, find each derivative and simplify.
The total cost (in hundreds of dollars) of producing x cameras per week is C(x) = 6 + √4x + 4 0 ≤ x ≤30 (A) Find C'(x). (B) Find C'(15) and C'(24). Interpret the results.
The number x of bicycle helmets people are willing to buy per week from a retail chain at a price of $p is given byx = 1,000 - 60p + 25 20 ¤ p ¤ 100(see the figure).(A) Find dx/dp. (B) Find the demand and the instantaneous rate of change of demand with
The use of iodine crystals is a popular way of making small quantities of water safe to drink. Crystals placed in a 1-ounce bottle of water will dissolve until the solution is saturated. After saturation, half of the solution is poured into a quart container of water, and after about an hour, the
A yeast culture at room temperature (68°F) is placed in a refrigerator set at a constant temperature of 38°F. After t hours, the temperature T of the culture is given approximately by T = 30e-0.58t + 38 t ≥ 0 What is the rate of change of temperature of the culture at the end of 1 hour? At the
In Problem, use implicit differentiation to find yʹ and evaluate yʹ at the indicated point. y2 - y - 4x = 0; (0,1)
In Problem, use implicit differentiation to find yʹ and evaluate yʹ at the indicated point. 3xy - 2x - 2 = 0; (2,1)
In Problem, use implicit differentiation to find yʹ and evaluate yʹ at the indicated point. 2y + xy - 1 = 0; (-1,1)
In Problem, use implicit differentiation to find yʹ and evaluate yʹ at the indicated point. 2x3y - x3 + 5 - 0; (-1,3)
In Problem, use implicit differentiation to find yʹ and evaluate yʹ at the indicated point. x2 - y = 4ey; (2,0)
In Problem find y' in two ways: (A) Differentiate the given equation implicitly and then solve for y'. (B) Solve the given equation for y and then differentiate directly. -2x + 6y -4 = 0
In Problem, use implicit differentiation to find yʹ and evaluate yʹ at the indicated point. In y = 2y2 - x; (2,1)
In Problem, use implicit differentiation to find yʹ and evaluate yʹ at the indicated point. xey - y = x2-2; (2,0)
Problems 23 and 24, find x' for x = x(t) defined implicitly by the given equation. Evaluate x' at the indicated point. x3 - tx2 -4 = 0;(-3, -2)
Find the slopes of the tangent lines at the points on the graph where x = 0.2. Check your answers by visually estimating the slopes on the graph in the figure.Refer to the equation and graph shown in the figure.
In Problem, find the equation(s) of the tangent line(s) to the graphs of the indicated equations at the point(s) with the given value of x. 3x + xy + 1 = 0; x = -1
In Problem, find the equation(s) of the tangent line(s) to the graphs of the indicated equations at the point(s) with the given value of x. xy2 - y - 2 = 0; x = 1
Explain the difficulty that arises in solving x3 + y + xey = 1 for y as an explicit function of x. Find the slope of the tangent line to the graph of the equation at the point (0,1).
In Problem, find y' and the slope of the tangent line to the graph of each equation at the indicated point. (y - 3)4- x = y;(-3,4)
In Problem, find y' and the slope of the tangent line to the graph of each equation at the indicated point. (2x - y)4 - y3 = 8 ;( -1. -2)
In Problem, find y' and the slope of the tangent line to the graph of each equation at the indicated point. 6√y3 + 1 - 2x3/2 -2 = 0; (4,2)
In Problem find y' in two ways: (A) Differentiate the given equation implicitly and then solve for y'. (B) Solve the given equation for y and then differentiate directly. 2x3 + 5y -2 = 0
In Problem, find y' and the slope of the tangent line to the graph of each equation at the indicated point. exy - 2x = y + 1; (0,0)
Refer to the equation in Problem 41. Find the equation(s) of the tangent line(s) at the point (s) on the graph where y = -1. Round all approximate values to two decimal places. Problelm 41 Find the equation(s) of the tangent line(s) at the point(s) on the graph of the equation y3 - xy - x3 =
For the demand equations in Problem, find the rate of change of p with respect to x by differentiating implicitly (x is the number of items that can be sold at a price of $p). x = p3 - 3p2 + 200
For the demand equations in Problem, find the rate of change of p with respect to x by differentiating implicitly (x is the number of items that can be sold at a price of $p). x = 3√1,500 - p3
In Problem 47, find dV/dL by implicit differentiation. Problem 47 In biophysics, the equation (L+m){V+n)= k is called the fundamental equation of muscle contraction, where m, n, and k are constants and V is the velocity of the shortening of muscle fibers for a muscle subjected to a load L. Find
The equationis Newton's law of universal gravitation. G is a constant and F is the gravitational force between two objects having masses m1 and m2 that are a distance r from each other. Use implicit differentiation to find dr/dF. Assume that m1 and m2 are constant.
Refer to Problem 50.Find dF/dr and discuss the connection between dF/dr and dr/dF.Problem 50The equationis Newton's law of universal gravitation. G is a constant and F is the gravitational force between two objects having masses m1 and m2 that are a distance r from each other. Use implicit
In Problem, use implicit differentiation to find yʹ and evaluate yʹ at the indicated point. 5x3 - y - 1 = 0; (1, 4)
In Problem, use implicit differentiation to find yʹ and evaluate yʹ at the indicated point. y2 - x3 - 4 = 0; (-2, 2)
Refer to Problem 9. Suppose that the distance between the boat and the dock is decreasing by 3.05 feet per second. How fast is the rope being pulled in when the boat is 10 feet from the dock?Problem 9A boat is being pulled toward a dock as shown in the figure. If the rope is being pulled in at 3
Refer to Problem 11. How fast is the circumference of a circular ripple changing when the radius is 10 feet? [Use C = 2πR, π ≈ 3.14.] Problem 11 A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is increasing by 2 feet per second, how fast is the area
Refer to Problem 13. How fast is the surface area of the sphere increasing when the radius is 10 centimeters? [Use S = 4TTR2, TT * 3.14.] Problem 13 The radius of a spherical balloon is increasing at the rate of 3 centimeters per minute. How fast is the volume changing when the radius is 10
Boyle's law for enclosed gases states that if the temperature is kept constant, the pressure P and volume V of a gas are related by the equation VP = k where k is a constant. If the volume is decreasing by 5 cubic inches per second, what is the rate of change of pressure when the volume is 1,000
A weather balloon is rising vertically at the rate of 5 meters per second. An observer is standing on the ground 300 meters from where the balloon was released. At what rate is the distance between the observer and the balloon changing when the balloon is 400 meters high?
In Problem Assume that x = x(t) and y = y(t). find the indicated rate, given the other information. 2. y = x3 - 3; dx/dt = -2when x = 2; find dy/dr
Refer to Problem 19. At what rate is the person's shadow growing when he is 20 feet from the pole? Problem 19 A streetlight is on top of a 20-foot pole. A person who is 5 feet tall walks away from the pole at the rate of 5 feet per second. At what rate is the tip of the person's shadow moving away
A point is moving along the x axis at a constant rate of 5 units per second. At which point is its distance from (0,1) increasing at a rate of 2 units per second? At 4 units per second? At 5 units per second? At 10 units per second? Explain.
A point is moving on the graph of x3+ y2= 1 in such a way that its y coordinate is always increasing at a rate of 2 units per second. At which point(s) is the x coordinate increasing at a rate of 1 unit per second?
Repeat Problem 25 for C = 72,000 + 60x R = 200x - x2/30 P = R - C Where production is increasing at a rate of 500 calculators per week at a production level of 1,500 calculators. Problem 25 Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are given by C
. Repeat Problem 27 for s = 50,000 - 20,000e-0.0004x Problem 27 A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are related by 5 = 60,000 - 40,000e-0.0005x The current weekly advertising costs are $2,000, and these costs are increasing at the rate of
Repeat Problem 29 for x2+2xp + 25p2 = 74,500 Problem29 The price p (in dollars) and demand x for a product are related by 2x2 + 5xp+ 50p2 = 80,000 (A) If the price is increasing at a rate of $2 per month when the price is $30, find the rate of change of the demand. (B) If the demand is decreasing
A person who is new on an assembly line performs an operation in T minutes after JC performances of the operation, as given byIf dx/dt = 6 operations per hours, where t is time in hours, find dT/dt after 36 performances of the operation.
In Problem Assume that x = x(t) and y = y(t). find the indicated rate, given the other information. 4. x2 + y2 = 4; dy/dt = 5 when x = 1.2 and y = -1.6; find dx/dt
In Problem Assume that x = x(t) and y = y(t). find the indicated rate, given the other information. 6. x2 - 2xy - y2 = 7; dy/df = -1 when x = 2 and y = -1; find dx/dt
A point is moving on the graph of 4x2 + 9y2 = 36. When the point is at (3,0), its y coordinate is decreasing by 2 units per second. How fast is its x coordinate changing at that moment?
Find the indicated derivatives in the following 12. d/dx(x6 In x) 14. y for y =In(2x3 - 3x)
In Problem, find the relative rate of change of fix) at the indicated value of x. Round to three decimal places. f{x) = 9x - 5 In A; x = 7
In Problem, find the percentage rate of change of f(x) at the indicated value of x. Round to nearest tenth of a percent. 18. f (x) = 75 +110x 20. f (x) = 75 +110x
In Problem, find the relative rate of change of fix). 2. f(x)=60x - 1.2x2 4. f{x)=15 - 3e-0.5x
In Problem, find the percentage rate of change of f(x) at the indicated value of x. Round to nearest tenth of a percent. 22. f (x) = 3,000 − 8x2 24. f (x) = 3,000 − 8x2
In Problem, use the price - demand equation to find E(p), the elasticity of demand. x = f(p) = 10,000 - 190p
In Problem, use the price - demand equation to find E(p), the elasticity of demand. x = f(p) = 8,400 - 7p2
In Problem, use the price - demand equation to find E(p), the elasticity of demand. x = f(p) = 160 - 35 In p
In Problem, use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p. A = f{p)= 1,875 - p2 (A) p = 15 (B) p = 25 (C) p = 40
In Problem, use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p. x = f{p)= 875 - p- 0.05p2 (A) p = 50 (B) p = 70 (C) p = 100
Given the price-demand equation p + 0.01x = 50 (A) Express the demand A as a function of the price p. (B) Find the elasticity of demand, E(p). (C) What is the elasticity of demand when p = $10? If this price is decreased by 5%, what is the approximate change in demand? (D) What is the elasticity of
Repeat Problem 37 for the price - demand equation 0.025x + p = 50 Problem 37 Given the price-demand equation 0.02x + p = 60 (A) Express the demand A as a function of the price p. (B) Express the revenue R as a function of the price p. (C) Find the elasticity of demand, E(p). (D) For which values of
In Problem, use the price-demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive. x = f(p) = 480 - 8p
In Problem, use the price-demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive. x = f(p) = 2,400 - 6p2
In Problem, use the price-demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive. x = f(p) = √324 - 2p
In Problem, use the price-demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive. x = f(p) = √3600 - 2p2
In Problem, use the demand equation to find the revenue function. Sketch the graph of the revenue function, and indicate the regions of inelastic and elastic demand on the graph. x = f(p) = 10(16 - p)
In Problem, use the demand equation to find the revenue function. Sketch the graph of the revenue function, and indicate the regions of inelastic and elastic demand on the graph. x = f(p) = 10 - (p - 9)2
In Problem, use the demand equation to find the revenue function. Sketch the graph of the revenue function, and indicate the regions of inelastic and elastic demand on the graph. x = f(p) = 30 - 5√p
If a price-demand equation is solved for p, then price is expressed as p = g(x) and x becomes the independent variable. In this case, it can be shown that the elasticity of demand is given byIn Problem, use the price-demand equation to find E(x) at the indicated value of x. P = g(x) = 30 - 0.05x, x
If a price-demand equation is solved for p, then price is expressed as p = g(x) and x becomes the independent variable. In this case, it can be shown that the elasticity of demand is given byIn Problem, use the price-demand equation to find E(x) at the indicated value of x. P = g(x)=20 -
In Problem, use the price-demand equation to find the values of x for which demand is elastic and for which demand is inelastic. p=g(x)=640 - 0.4x
In Problem, find the relative rate of change of fix). f (x) = 25 − 2ln x
In Problem, use the price-demand equation to find the values of x for which demand is elastic and for which demand is inelastic. p=g(x)=540 - 0.2x2
Refer to Problem 65. If the current price of a hamburger is $4.00, will a 10% price increase cause revenue to increase or decrease? Problem 65 The price-demand equation for hamburgers at a fast-food restaurant is x + 400p = 3,000 Currently, the price of a hamburger is $3.00. If the price is
Refer to Problem 67. If the current price of an order of fries is $1.29, will a 10% price decrease cause revenue to increase or decrease? Problem 67 The price-demand equation for an order of fries at a fast-food restaurant is x+ l,000p = 2,500 Currently, the price of an order of fries is $0.99. If
Refer to Problem 67. What price will maximize the revenue from selling fries? Problem 67 The price-demand equation for an order of fries at a fast-food restaurant is x + l,000p = 2,500 Currently, the price of an order of fries is $0.99. If the price is decreased by 10%, will revenue increase or
A model for Mexico's population growth (Table 4) isF(t) = 1.49t + 38.8 where t is years since 1960. Find and graph the percentage rate of change of f(t) for 0 ¤ t ¤ 50.
A model for the number of assaults in the United States (Table 5) is a(t) = 18.2 - 5.2 Int where t is years since 1990. Find the relative rate of change for assaults in 2008.
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