The cost (in dollars) of producing x units of a certain com-...

Name: Problem 51, Chapter 2: Calculus
Uploaded: 2020-07-10T15:09:06-08:00
Duration: 2 min 44 s
Channel: Benjamin Schreyer

The cost (in dollars) of producing $x$ units of a certain com- modity 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 $2.7 . )$

The cost (in dollars) of producing $x$ units of a certain com-
modity 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 $2.7 . )$