   Chapter 14.3, Problem 9E Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Solutions

Chapter
Section Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

If the joint cost function for two products is C ( x , y )= x y 2 + 1 dollars (a) find the marginal cost (function) with respect to x.(b) find the marginal cost with respect to y.

(a)

To determine

To calculate: The marginal cost with respect to x if the joint cost function for two products is given by C(x,y)=xy2+1 dollars.

Explanation

Given Information:

The joint cost function for two products is given by C(x,y)=xy2+1 dollars.

Formula used:

For a joint cost function of the form C(x,y), the marginal cost with respect to x is given by Cx and the marginal cost with respect to y is given by Cy.

For a function f(x,y), the partial derivative of f with respect to x is calculated by taking the derivative of f(x,y) with respect to x and keeping the other variable y constant. The partial derivative of f with respect to x is denoted by fx.

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

Chain rule for the function f(x)=u(v(x)) is f(x)=u(v(x))v(x).

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

The coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x)

(b)

To determine

To calculate: The marginal cost with respect to y if the joint cost function for two products is given by C(x,y)=xy2+1 dollars.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Write the sum in expanded form. 5. k=042k12k+1

Single Variable Calculus: Early Transcendentals, Volume I 