The cost function for the manufacture of x number of goods by a company is given by:
\(C(x)=2x^3-9x^2+12x+1\), then the value of x at which marginal cost is minimum is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{3}{2}\)
The marginal cost is the derivative of the cost function:
\(MC = C'(x) = 6x^2 - 18x + 12\)
To minimise MC, differentiate MC itself:
\( \displaystyle \frac{d(MC)}{dx} = 12x - 18 = 0,\quad x = \frac{3}{2} \)
\( \displaystyle \frac{d^2(MC)}{dx^2} = 12 \gt 0 \)
So MC is minimum at \(x = \frac{3}{2}\).
CBSE Applied Mathematics (Class XII):
Maxima and Minima
