If $C(x)=x^3-\frac{5}{2}x^2 +10$ represents the total cost of producing x units by a car manufacturing company. The slope of the marginal cost curve at $x=3$, will be :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 13
$C(x)=x^3-\frac{5}{2}x^2+10$
Marginal Cost = $\frac{d}{dx}C(x)$
$C'(x)=3x^2-5x=MC(x)$
Slope of Marginal Cost Curve = $\frac{d}{dx}C'(x)$
$MC'(x)=\frac{d}{dx}(3x^2-5x)$
$=6x-5$
$MC'(3)=18-5=13$