Question

The value of $C$ in Mean value theorem for the function $f\left(x\right)=x^2$ in $\in [2,4]$ is

• A. $3$
• B. $2$
• C. $4$
• D. $\frac{7}{2}$

Answer 1

The correct option is A $3$

Using the Mean Value Theorem
$f^{\prime }\left(C\right)=\frac{f\left(4\right)-f\left(2\right)}{4-2}$
$\Rightarrow 2C=6$
$\Rightarrow C=3$