Given that the total cost function for \( x \) units of a commodity is \( C(x)=\displaystyle\frac{x^{3}}{4}+4x^{2}-8x+20 \). Then the marginal cost when \( x=4 \) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 36
Marginal cost is the derivative of the total cost function.
\( \displaystyle MC=\frac{dC}{dx}=\frac{3x^{2}}{4}+8x-8 \)
At x = 4:
\( \displaystyle MC=\frac{3(16)}{4}+8(4)-8 \)
\( \displaystyle MC=12+32-8=36 \)