Question

If f(x) is differentiable in the interval [2, 5] and $f\left(2\right)=\frac{1}{5};f\left(5\right)=\frac{1}{2}$. Then there exist a number ‘c’, 2 < c < 5 for which f’(c) is equal to

• A. $\frac{1}{2}$
• B. $\frac{1}{5}$
• C. $\frac{1}{10}$
• D. $\frac{1}{7}$

Answer 1

The correct option is C $\frac{1}{10}$

$f^{{}^{\prime }}\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$
$=\frac{\frac{1}{2}-\frac{1}{5}}{3}=\frac{1}{10}$