For a manufacturer, total cost function is given by $c=\frac{x^2}{25}+2x.$ Which of the following are correct ?

A. 2.6 is the marginal cost when 5 units are produces.

B. $\frac{2x}{25}+2 $ is the average cost function.

C. $\frac{x}{25}+2 $ is the average cost function.

D. 2.4 is the marginal cost when 5 units are produced.

E. $\frac{x}{25}+1 $ is the average cost function.

Choose the correct answer from the options given below:

C, D only

Given total cost

$C=\frac{x^2}{25}+2x$

Marginal cost

$MC=\frac{dC}{dx}$

$MC=\frac{2x}{25}+2$

At $x=5$

$MC=\frac{2(5)}{25}+2$

$=\frac{10}{25}+2$

$=0.4+2=2.4$

So statement (D) is correct and (A) is incorrect.

Average cost

$AC=\frac{C}{x}$

$AC=\frac{\frac{x^2}{25}+2x}{x}$

$AC=\frac{x}{25}+2$

So statement (C) is correct.

The correct statements are (C) and (D).