The total cost of a firm is given by \(C(x)=\displaystyle\frac{2x^3}{3}-4x^2+8x+7\). The level of output at which marginal cost is minimum is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
The marginal cost is the derivative of the total cost:
\(MC = C'(x) = 2x^2 - 8x + 8\)
To make MC minimum, its own derivative is set to 0:
\( \displaystyle \frac{d(MC)}{dx} = 4x - 8 = 0 \Rightarrow x = 2 \)
\( \displaystyle \frac{d^2(MC)}{dx^2} = 4 \gt 0 \)
So MC is minimum at an output of x = 2.
CBSE Applied Mathematics (Class XII):
Maxima and Minima
