If the marginal cost is given by function MC(x) = $\frac{x}{2}+3$
Which of the following can be the cost function?
A. $\frac{x^2}{4}+3$
B. $\frac{x^2}{4}+3 x+5$
C. $\frac{x^2+12 x-1}{4}$
D. $\frac{1}{2}$
E. $\frac{x^2}{4}-3 x-1$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option () -
$MC(x)=\frac{x}{2}+3.$
$\text{Cost function }C(x)=\int MC(x)\,dx.$
$C(x)=\int\left(\frac{x}{2}+3\right)dx.$
$C(x)=\frac{x^2}{4}+3x+C.$
$\text{Any constant }C\text{ is admissible.}$
$\text{Option B: }\frac{x^2}{4}+3x+5 \text{ matches.}$
$\text{Option C: }\frac{x^2+12x-1}{4}=\frac{x^2}{4}+3x-\frac{1}{4} \text{ also matches.}$
$\text{Correct options: B and C.}$