If $C(x)=\frac{1}{3}x^3+x^2-15x+3000$ is the cost function then the minimum value of marginal cost function is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → -16
The Marginal Cost function is,
$MC(x)=\frac{d}{dx}C(x)=\frac{d}{dx}\left(\frac{1}{3}x^3+x^2-15x+3000\right)$
$=x^2+2x-15$
for critical point,
$f'(c)=0$
$⇒2x+2=0$
$⇒x=-1$
$∴MC(-1)=(-1)^2+2(-1)-15$
$=-16$ → Minimum Value