Question

If $f\left(x\right)$ is differentiable in the interval $[2,5]$, where $f\left(2\right)=\frac{1}{5}$ and $f\left(5\right)=\frac{1}{2}$, then there exists a number $c$, $2<c<5$ for which $f^{\prime }\left(c\right)=$

• A. $\frac{1}{2}$
• B. $\frac{1}{5}$
• C. $\frac{1}{10}$
• D. None

Answer 1

Answer: (C)

$\frac{1}{10}$

For
$2<c<5$
$f^{\prime }\left(c\right)=\frac{f\left(5\right)-f\left(2\right)}{5-2}$
$=\frac{0.5-0.2}{3}$
$=\frac{0.3}{3}$
$=0.1$
$=\frac{1}{10}$