   Chapter 11.2, Problem 36E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

For the cost function C ( x ) = m x + b themarginal cost of producing the 1,001st item is(A) equal to(B) approximately equal to(C) always slightly greater than(D) always slightly less than the actual cost of producing the 1,001st item.

To determine

The relation between marginal cost of producing the 1,001st item and the actual cost of producing 1,001st item for the cost function C(x)=mx+b from the following options:

Explanation

Given Information:

The cost function is C(x)=mx+b.

The provided choices are,

(A) Equal to

(B) Approximately equal to

(C) Always slightly greater than

(D) Always slightly less than

Consider the cost function, C(x)=mx+b

Calculate marginal cost.

As, the marginal cost is the derivative of the function,

C(x)=ddx(mx+b)

Constant multiple rule of derivative of function f(x) is ddx[cf(x)]=cddx[f(x)] where c is constant.

Sum rule of derivative is ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)] where, f(x) and g(x) are any two differentiable functions.

So,

Apply sum rule and constant multiple rule of derivative,

C(x)=mddx(x)+bddx(1)

Derivative of function using power rule, y=xn is dydx=nxn1

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