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mathematics
mathematical applications for the management
Mathematical Applications For The Management, Life And Social Sciences 12th Edition Ronald J. Harshbarger, James J. Reynolds - Solutions
Find the derivatives of the functions in Problem. 1 + e5x ソ= 3x
In Problem, find y'.y = ln (x4 + 3)2
In Problem, find y'. y = log4 x
The table gives the number of women age 16 years or older (in millions) in the U.S. civilian workforce for selected years from 1950 and projected to 2050.(a) Use x as the number of years past 1950 to create a cubic model using these data. Report the model with three significant digit
The total cost function for a product is C = 2x2 + 54x + 98. How many units must be produced to minimize average cost?
If in Problem 40 the mountain bikes cost the shop $1360 each, at what selling price will MMR II’s profit be a maximum?
In Problem, use the derivative to locate critical points and determine a viewing window that shows all features of the graph. Use a graphing calculator to sketch a complete graph.y = 7 + 3x5 - 5x6
The following table gives the value (in billions of dollars) of U.S. industrial shipments for selected years from 2014 and projected to 2040.(a) Find a cubic function that models these data, with x as the number of years after 2010 and y as the billions of dollars of U.S. industrial shipments.
The following table gives the millions of metric tons of carbon dioxide emissions from biomass energy combustion in the United States for selected years from 2010 and projected to 2032.(a) Create a cubic function that models these data, with x as the number of years past 2010 and y as the millions
In Problem, find the derivative of each function.y = 5ex3 + x2
In Problem, find the derivative of each function.y = 4 ln (x3 + 1)
In Problem, find the derivative of each function.y = ln (x4 + 1)3
In Problem, find the derivative of each function.f (x) = 10(32x)
In Problem, find the derivative of each function.S = tet4
In Problem, find the derivative of each function.g (x) = (2e3x+1 - 5)3
In Problem, find the derivative of each function.y = ex3+1/x
Find the derivatives of the functions in Problem.f (x) = ln x3
In Problem, find the derivative of each function.s = 3/4 ln (x12 - 2x4 + 5)
In Problem, find the derivative of each function.y = 3 ln x/x4
Find the derivatives of the functions in Problem.f(x) = ln (4x + 9)
Find the derivatives of the functions in Problem.y = ex3
Find the derivatives of the functions in Problem. y = et? - 1
In Problem, find the derivative of each function.w = (t2 + 1) ln (t2 + 1) - t2
In Problem, find the derivative of each function.g (x) = 2 log5 (4x + 7)
Find the derivatives of the functions in Problem.y = ln (6x + 1)
Find the derivatives of the functions in Problem. ソミ 6e3x?
In Problem, find the derivative of each function.y = 33x-4
Find y' if 3x4 + 2y2 + 10 = 0.
Find the derivatives of the functions in Problem.y = ln (2x2 - x) + 3x
In Problem, find the derivative of each function.y = 1 + log8 (x10)
Let x2 + y2 = 100.If dx/dt = 2, find dy/dt when x = 6 and y = 8.
Find the derivatives of the functions in Problem.y = ln (8x3 - 2x) - 2x
Find the derivatives of the functions in Problem. y 2e(x2 + 1)3
In Problem, find the derivative of each function.y = lnx/x
Find y' if xey = 10y.
Find dp/dq if p = ln (q2 + 1).
Find the derivatives of the functions in Problem. y = e√x2 -9
In Problem, the demand functions for specialty steel products are given, where p is in dollars and q is the number of units. For both problems(a) find the elasticity of demand as a function of the quantity demanded, q.(b) find the point at which the demand is of unitary elasticity and find
In Problem, find the derivative of each function. 1 + e-x y 1 - e-*
Suppose the weekly revenue and weekly cost (both in dollars) for a product are given byR(x) = 300x - 0.001x2 and C(x) = 4000 + 30x,respectively, where x is the number of units produced and sold. Find the rate at which profit is changing with respect to time when the number of units produced and
If p2 + 4p - q = 4, find dp/dq.
Find ds/dq if s = ln (q2/4 + 1).
Find the derivatives of the functions in Problem.y = eln x3
Write the equation of the line tangent to y = 4ex3 at x = 1.
Suppose the demand for a product is p2 + 3p + q = 1500, where p is in dollars and q is the number of units. Find the elasticity of demand at p = 30. If the price is raised to $31, does revenue increase or decrease?
If xy2 - y3 = 1, find y'.
Find the derivatives of the functions in Problem.y = e3 1 eln x
At x = 1, write the equation of the line tangent toy = 8 + 3x2 ln x.
Suppose the demand function for a product is given by (p + 1)q2 = 10,000, where p is the price, and q is the quantity. Find the rate of change of quantity with respect to price when p = $99.
If p2 - q = 4, find dp/dq.
Find the derivatives of the functions in Problem.y = e-1/x
In Problem, p is the price per unit in dollars and q is the number of units. If the weekly demand function is p = 30 - q and the supply function before taxation is p = 6 + 2q, what tax per item will maximize the total tax revenue?
The sales of a product are given by S = 80,000e-0.4t, where S is the daily sales and t is the number of days after the end of an advertising campaign. Find the rate of sales decay 10 days after the end of the ad campaign.
If p2q = 4p - 2, find dp/dq.
Find the derivatives of the functions in Problem.y = 2e√x
Using U.S. Centers for Medicare and Medicaid Services data from 2000 and projected to 2024, the total U.S. expenditures (in billions of dollars) for professional health services and retail medical products (includingprescription drugs) can be modeled byy = 617e0.0505twhere t is the number of years
If x2 - 3y4 = 2x5 + 7y3 - 5, find dy/dx.
In each of Problem, find the derivative of the function in part (a). Then find the derivative of the function in part (b) or show that the function in part (b) is the same function as that in part (a).(a) y = 3 ln (x4 - 1)(b) y = ln (x4 - 1)3
Find the derivatives of the functions in Problem.y = e-1/x2 + e-x2
Suppose the demand and supply functions for a product are p = 1100 - 5q and p = 20 + 0.4q, respectively, where p is in dollars and q is the number of units. Find the tax per unit t that will maximize the tax revenue T = tq.
If 3x5 - 5y3 = 5x2 + 3y5, find dy/dx.
In each of Problem, find the derivative of the function in part (a). Then find the derivative of the function in part (b) or show that the function in part (b) is the same function as that in part (a).(a) y = ln (4x - 1) - 3 ln x(b) y = ln (4x - 1/x3)
Find the derivatives of the functions in Problem.y = 2/e2x + e2x/2
Projections indicate that the percent of U.S. adults with diabetes will dramatically increase. The table gives the percent of U.S. adults with diabetes for selected years from 2010 and projected to 2050.(a) Find a logarithmic model, y = f (x), for these data. Use x as the number of years after
In each of Problem, find the derivative of the function in part (a). Then find the derivative of the function in part (b) or show that the function in part (b) is the same function as that in part (a).(a) y = 3 ln x - ln (x + 1)(b) y = ln (x3/x + 1)
Find the derivatives of the functions in Problem.s = t2et
Prices for goods and services tend to rise over time, and this results in the erosion of purchasing power. With the 2012 dollar as a reference, purchasing power of 0.921 for a certain year means that in that year, a dollar will purchase 92.1% of the goods and services that could be purchased for $1
If x4 + 2x3y2 = x - y3, find dy/dx.
Find dp/dq if p = ln (q2 - 1/q).
Find the derivatives of the functions in Problem.p = 4qeq3
In Problem, find the indicated derivative.Find the second derivative y" if x2 + y2 = 1.
If (x + y)2 = 5x4y3, find dy/dx.
Find ds/dt if s = ln [t3(t2 - 1)].
The supply function for a product is given by p = 40 + 100√2x + 9, where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when the price per unit is $740?
Find the derivatives of the functions in Problem.y = ex4 - (ex)4
Find dy/dx for x4 + 3x3y2 - 2y5 = (2x + 3y)2.
Find dy/dt if y = ln (t2 + 3/√1 - t).
Find the derivatives of the functions in Problem.y = 4(ex)3 - 4ex3
Find y' for 2x + 2y = √x2 + y2.
Find dy/dx if y = ln (x3√x + 1).
Find the derivatives of the functions in Problem.y = ln (e2x + 1)
For Problems, find the slope of the line tangent to the curve.2x2 - 10x + 2y3 + 14 = 0 at (3, -1)
Find dy/dx if y = ln [x2(x4 - x + 1)].
Find the derivatives of the functions in Problem.y = e-3x ln (2x)
Find the derivatives of the functions in Problem.y = e2x2 ln (4x)
For Problems, find the slope of the line tangent to the curve.y2 + 2x2 + 4xy + 7 = 0 at (-2, 3)
Find the derivatives of the functions in Problem. ソ= 1 + e2*
In Problem, wriIn Problem, write the equation of the tangent line to each curve at the given point.x2 + y2 + 6x - 3y + 7 = 0 at (-1, 2)
Find the derivatives of the functions in Problem.y = (e3x + 4)10
In Problem, write the equation of the tangent line to each curve at the given point.4x2 - 2y2 + 3xy - 3x = 26 at (-2, -1)
Find the derivatives of the functions in Problem. et ソ= et + e - e-* ーX ーX
In Problem, write the equation of the tangent line to each curve at the given point.8xy + y2 - x2 + 38x = 217 at (3, 4)
In Problem, find y'.y = ln (3x + 1)1/2
Find the derivatives of the functions in Problem.y = 6x
In Problem, find y'.y = (ln x)4
Find the derivatives of the functions in Problem.y = 3x
In Problem, find y'.y = (ln x)-1
Find the derivatives of the functions in Problem. y = 4x2
In Problem, find y'.y = [ln (x4 + 3)]2
Find the derivatives of the functions in Problem.y = 52x - 1
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