A manufacturing company’s total production cost in dollars for producing thousand…

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A manufacturing company’s total production cost in dollars for producing

p

thousand smartphone cases is modeled by the differentiable function

C(p)

. Management knows that

C(100)=1.20\times10^{6}\,\text{dollars}

and

C'(100)=7.5\times10^{3}

. Answer the following. (a) Identify the units of

C'(100)

. (b) Interpret the meaning of

C'(100)=7.5\times10^{3}

in the context of the company’s production. (c) Describe how the instantaneous rate of change represented by

C'(100)

differs conceptually from the average rate of change of

C

over the interval

90\le p\le110

. No numerical calculation of the average rate is required.