For the function f(x) = e^x ,a = 0,b = 1, the value of c in mean … - Vidyadip

MCQ

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

A
$log \,x$
✓
$\log (e - 1)$
C
$0$
D
$1$

✓

Answer

Correct option: B.

$\log (e - 1)$

b
(b) Here $\frac{{f(b) - f(a)}}{{b - a}} = f'(c)$

==> $\frac{{{e^b} - {e^a}}}{{b - a}} = f'(c)$

==>$\frac{{e - 1}}{{1 - 0}} = {e^c} \Rightarrow c = \log (e - 1)$.

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