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mathematics
college mathematics for business economics

Questions and Answers of College Mathematics For Business Economics

Find the indicated derivatives in Problems 34–36. d dx -logs (x² - x)
In Problems 17-38, find f'(x) and simplify. f(x) = 3 ln(1 + x²)
In Problems 35–46, find h′(x), where f(x) is an unspecified differentiable function. h(x) = xf(x)
Find the indicated derivatives in Problems 34–36. d dx -Vin(x² + x)
In Problems 35–46, find h′(x), where f(x) is an unspecified differentiable function. h(x) = x²f(x)
A man with $20,000 to invest decides to diversify his investments by placing $10,000 in an account that earns 7.2% compounded continuously and $10,000 in an account that earns 8.4% compounded
In Problems 17-38, find f'(x) and simplify. f(x) = (x2 ln x) 4
A rock thrown into a still pond causes a circular ripple. The radius is increasing at a constant rate of 3 feet per second. Show that the area does not increase at a constant rate. When is the rate
In Problems 35–46, find h′(x), where f(x) is an unspecified differentiable function. h (x) f(x)
A point moves along the graph of y = x3 in such a way that its y coordinate is increasing at a constant rate of 5 units per second. Does the x coordinate ever increase at a faster rate than the y
In Problems 35–46, find h′(x), where f(x) is an unspecified differentiable function. h(x) = f(x) x² 2
In Problems 39–46, find the logarithmic derivative. A(t) = 500e0.07t
How long will it take money to double if it is invested at 10% interest compounded.(A) Semi-annually? (B) Continuously?
If $100 is invested at 8% interest compounded annually, then the amount (in dollars) at the end of t years is given by A = 100 (1.08)¹ Find A' (1), A'(2), and A'(10).
In Problems 39–46, find the logarithmic derivative. A(t) = 2,000e0.052t
In Problems 39–46, find the logarithmic derivative. A(t) = 3,500e0.15t
In Problems 41-48, find y' and the slope of the tangent line to the graph of each equation at the indicated point. (x - 2y)³ = 2y²-3; (1, 1)
Given the demand equation find the rate of change of p with respect to x by implicit differentiation (x is the number of items that can be sold at a price of $p per item). x = V5,000 2p³ -
In Problems 75–92, find each indicated derivative and simplify. f(w) = ) = (w + 1)2
In Problems 75-78, give the domain off, the domain of g, and the domain of m, where m(x) = f[g(x)]. f(u) = = In u; g(x) = 2x + 10
In Problems 75-78, give the domain off, the domain of g, and the domain of m, where m(x) = f[g(x)]. f(u) = 1 u² - 1 -;g(x) = ln x
In Problems 75–92, find each indicated derivative and simplify. dy dx for y=9x¹/3(x³ + 5)
In Problems 75-78, give the domain off, the domain of g, and the domain of m, where m(x) = f[g(x)]. n 6 - x = (x)8 : 2: 1 (n)f
In Problems 75–92, find each indicated derivative and simplify. d -[(4x¹/2 - 1) (3x¹/3 + 2)] dx
In Problems 75–92, find each indicated derivative and simplify. y' for y log₂ x 1 + x²
In Problems 75–92, find each indicated derivative and simplify. dy dx for y= 10⁰ 1+x+
In Problems 79-90, find each derivative and simplify. 2x³ 3 xp (L x) P t
In Problems 75–92, find each indicated derivative and simplify. f'(x) for f(x) = 6³√x 2 x²-3
In Problems 75–92, find each indicated derivative and simplify. y' for y= 2Vx x²-3x + 1
In Problems 79-90, find each derivative and simplify. d dx log₂ (3x² - 1)
In Problems 75–92, find each indicated derivative and simplify. g' (t) if g(t) 0.2t 31² 1
In Problems 79-90, find each derivative and simplify. d dx -log (x³ - 1)
In Problems 75–92, find each indicated derivative and simplify. d dx [4x log x³]
In Problems 75–92, find each indicated derivative and simplify. d x³ - 2x² dx ZA
In Problems 75–92, find each indicated derivative and simplify. f'(x) for f(x) = (2x² - 1) (x²+3) x² + 1 X
A research group using hospital records developed the following mathematical model relating systolic blood pressure and age:P(x) is pressure, measured in millimeters of mercury, and x is age in
In Problems 9 and 10, use the given information to sketch the graph of f. Assume that f is continuous on its domain and that all intercepts are included in the information given. Domain: All real
Find two numbers whose sum is 15 and whose product is a maximum.
In Problems 9 and 10, use the given information to sketch the graph of f. Assume that f is continuous on its domain and that all intercepts are included in the information given. Domain: All real x
Use the graph of y = f(x), assuming f"(x) > 0 if x = b or f, to identify.(A) Intervals on which the graph of f is concave upward (B) Intervals on which the graph of f is concave downward (C)
Use the graph of y = g(x), assuming g"(x) > 0 if x = c or g, to identify.(A) Intervals on which the graph of g is concave upward. (B) Intervals on which the graph of g is concave downward. (C)
Find two numbers whose difference is 15 and whose product is a minimum.
Find f"(x) for f(x) = 3x2 + Inx.
In Problems 11–18, use the given information to sketch the graph of f. Assume that f is continuous on its domain and that all intercepts are included in the table of values. Domain: All real x;
Problems 9–16, refer to the following graph of y = f(x):Identify the intervals on which f = (x) b C d f(x) e f Figure for 9-16 8 h ·x
In Problems 11–18, use the given information to sketch the graph of f. Assume that f is continuous on its domain and that all intercepts are included in the table of values. Domain: All real x; lim
Find y" for y = 3x + 4/x .
Problems 9–16, refer to the following graph of y = f(x):Identify the intervals on which f = (x) > 0. a b C d f(x) MA h 8 e f Figure for 9-16 00 X
In Problems 13 and 14, find the domain and intercepts. f(x) || 2 + x 1 - x²
Find two positive numbers whose product is 15 and whose sum is a minimum.
In Problems 13 and 14, find the domain and intercepts. f(x) = ln(x + 2)
In Problems 15 and 16, find the horizontal and vertical asymptotes. f(x) = 2x + 5 2x² 32
Problems 9-18 refer to the graph of y = f(x) shown here. Find the absolute minimum and the absolute maximum over the indicated interval. f(x) 15 10 5 5 10 X
In Problems 15 and 16, find the horizontal and vertical asymptotes. f(x) = 2x - 7 3x + 10
In Problems 17–24, find the indicated derivative for each function. 2x³4x² + 5x - 6 f"(x) for f(x) = 2x³
In Problems 17–24, find the indicated derivative for each function. g"(x) for g(x) = -x³ + 2x² 3x + 9
In Problems 17–24, find the indicated derivative for each function. -1 h"(x) for h(x) = 2x¹3x-2
In Problems 17 and 18, find the x and y coordinates of all inflection points. f(x) = x4 - 16x3 + 10
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = x + 3 x - 3
In Problems 19 and 20, find (A) f'(x), (B) the partition numbers for f', and (C) the critical numbers of f. 2x¹/3-²/3 f(x) = 2x¹/3
In Problems 17–24, find the indicated derivative for each function. k" (x) for k(x) = -6x² + 12x-3
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 2x - 4 x + 2
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = X x-2
In Problems 17–24, find the indicated derivative for each function. d'y/dx² for y=x²³ - 24x¹/3
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) 2 + x 3-x
In Problems 17–24, find the indicated derivative for each function. y" for y= (x² + 9)4
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 5 + 5e-0.1x
In Problems 17–24, find the indicated derivative for each function. y" for y=(x²16)5
In Problems 23–26, find the absolute maximum and absolute minimum of each function on the given interval. f(x) = In x on [1, 2]
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 3 + 7e-0.2r
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 5xe-0.2x
In Problems 25–30, find the x and y coordinates of all inflection points. f(x) = x³ + 30x²
In Problems 23–26, find the absolute maximum and absolute minimum of each function on the given interval. f(x) = x² - 6x + 7 on [0, 10]
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 10xe-0.1x
In Problems 25–30, find the x and y coordinates of all inflection points. f(x) = x³ - 24x²
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = ln(1 x) -
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function.f(x) = x2 + 4x - 3
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x).f(x) = ln (2x + 4)
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function.f(x) = -x2 - 6x + 9
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = x - ln x
Find each limit in Problems 31–40. ln x lim >00 x5 x
In Problems 41-48, f(x) is continuous on (-∞,∞). Use the given information to sketch the graph of f. f'(x) f"(x) -4 f(x) 0 3 + + + 0 -2 - -2 3 - 1 1.5 2 1 - 0 +++ 0 2 0 0 - --- 2 -1 X X 4 -3
In Problems 43 - 66, find the indicated extremum of each function on the given interval. Absolute maximum value on (0, ∞ ) for x) = 2/²0 f(x)
In Problems 9–24, find each indefinite integral. Check by differentiating. [₁ 10 dx
In Problems 9–44, find each indefinite integral and check the result by differentiating. Jo (x² - 1)³(2x) dx
In Problems 65–70, find each indefinite integral. 2x dx
In Problems 59–70, find each indefinite integral and check the result by differentiating. et 1+ etdx
In Problems 59–70, find each indefinite integral and check the result by differentiating. [/2e-¹1 x xp x/1- dx
In Problems 65–70, find each indefinite integral. x²e¹ - 2x x² fire dx
In Problems 65–70, find each indefinite integral. 1 – xe dx X
In Problems 71–74, find the derivative or indefinite integral as indicated. dx (√x x²³ dx
In Problems 71–74, find the derivative or indefinite integral as indicated. In d (f ¹m² di) -dt dt
In Problems 71–74, find the derivative or indefinite integral as indicated. d Sa -(x4 + 3x² + 1) dx dx
In Problems 71–74, find the derivative or indefinite integral as indicated. d du ; (eu²³) пр
The graph of the marginal cost function from the production of x thousand bottles of sunscreen per month [where cost C(x) is in thousands of dollars per month] is given in the figure.(A) Using the
In Problems 9–24, find each indefinite integral. Check by differentiating. [ 14x dx
In Problems 9–24, find each indefinite integral. Check by differentiating. [15 15x² dx
In Problems 9–24, find each indefinite integral. Check by differentiating. [x² x dx
In Problems 9–24, find each indefinite integral. Check by differentiating. fot xdx
In Problems 9–24, find each indefinite integral. Check by differentiating. хр xp €/1X8 18

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