Chapter 2.7, Problem 51E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

The cost (in dollars) of producing *x* units of a certain commodity is *C(x)* = 5000 + 10*x* + 0.05*x*^{2}.

(a) Find the average rate of change of *C* with respect to *x* when the production level is changed

(i) from *x* = 100 to *x* = 105

(ii) from *x=* 100 to *x* = 101

(b) Find the instantaneous rate of change of *C* with respect to *x* when *x* = 100. (This is called the *marginal cost*. Its significance will be explained in Section 3.7.)

(a)

To determine

**To find:** The average rate of change of *x* is changed for the respected intervals.

Explanation

**Given:**

Let *x* units of a commodity.

The given cost function *.*

**Formula used:**

The average rate of change of *C* with respect to *x* on the interval

**Calculation:**

**Section (i)**

Obtain the average rate of change of

Substitute 100 for

(b)

To determine

**To estimate:** The instantaneous rate of change of *C* with respect to *x* when

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P-38RECh-2 P-39RECh-2 P-40RECh-2 P-41RECh-2 P-42RECh-2 P-43RECh-2 P-44RECh-2 P-45RECh-2 P-46RECh-2 P-47RECh-2 P-48RECh-2 P-49RECh-2 P-50RECh-2 P-51RECh-2 P-52RECh-2 P-53RECh-2 P-54RECh-2 P-1PCh-2 P-2PCh-2 P-3PCh-2 P-4PCh-2 P-5PCh-2 P-6PCh-2 P-7PCh-2 P-8PCh-2 P-9PCh-2 P-10PCh-2 P-11PCh-2 P-12PCh-2 P-13PCh-2 P-14P

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