Question

For the function $f\left(x\right)=e^x,a=0,b=1$, the value of $c$ in mean value theorem will be

• A. $0$
• B. $\log (e-1)$
• C. $\log x$
• D. $1$

Answer 1

Answer: (B)

$\log (e-1)$

Given, $f\left(x\right)=e^x,a-0,b=1$

Here, $\frac{f\left(b\right)-f\left(a\right)}{b-a}=f^{\prime }\left(c\right)$
$\Rightarrow \frac{e^b-e^a}{b-a}=f^{\prime }\left(c\right)$

$\Rightarrow \frac{e-1}{1-0}=f^{\prime }\left(c\right)$
$\Rightarrow c=\log (e-1)$