The total cost of a firm is given by $C(x)=\frac{2x^3}{3}-4x^2+8x+7.$ The level of output at which marginal cost in minimum is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{2}{3}$
The total cost is,
$C(x)=2x^3-4x^2+8x+7$
$MC=\frac{d}{dx}C(x)=6x^2-8x+8$
for minimum, $MC'(c)=0$
$⇒12x-8=0$
$⇒x=\frac{2}{3}$