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. log x
• B. log (e-1)
• C. 1

Answer 1

The correct option is B log (e-1)

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