Question

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

• A. 3
• B. 2
• C. 4
• D. 7/2

Answer 1

Answer: (A)

For mean value theorem
$ f'(c) =\frac{f(b)-f(a)}{b-a}$
$\therefore f(x) =x^{2} $
$ \Rightarrow \, f'(x) =2 x$
$\Rightarrow \, 2 c =\frac{f(4)-f(2)}{4-2}$
$ \Rightarrow \, 2 c =\frac{4^{2}-2^{2}}{4-2} $
$ \Rightarrow \, 2 c =4+2$
$ \Rightarrow \, 2 c =6$
$ c =3 $