If the cost function of a product is given by $C(x) =\frac{3}{4}x^2-5x+21$, then the marginal cost when $x = 10$ is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10
Given cost function: $C(x) = \frac{3}{4}x^2 - 5x + 21$
Marginal cost: $MC = \frac{dC}{dx} = \frac{d}{dx} \left(\frac{3}{4}x^2 - 5x + 21\right) = \frac{3}{2}x - 5$
At $x = 10$: $MC = \frac{3}{2} \cdot 10 - 5 = 15 - 5 = 10$