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 :

13

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 = $\frac{d}{dx}C'(x)$

$MC'(x)=\frac{d}{dx}(3x^2-5x)$

$=6x-5$

$MC'(3)=18-5=13$