The value of C, in Rolle's theorem for the function f(x) = e^x x, when x [0, ] is : Option 1: ()/6 Option 2: ()/4 Option 3: ()/2 Option 4: (3)/4

Answer: (3)/4. Solution: f(0)=0, f()=0, f continuous and differentiable, so Rolle's applies. f'(x)=e^x( x+ x)=0 x=-1. In [0,]: x=(3)/4.

Calculus

Application of Derivatives

Medium

core

The value of C, in Rolle's theorem for the function $f(x) = e^x \sin x$ , when $x \in [0, \pi]$ is :

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$\frac{3\pi}{4}$

✅ Correct Option: 4

$f(0)=0$ , $f(\pi)=0$ , $f$ continuous and differentiable, so Rolle's applies.

$f'(x)=e^x(\sin x+\cos x)=0 \Rightarrow \tan x=-1$ .

In $[0,\pi]$ : $x=\frac{3\pi}{4}$ .

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CUET Mathematics Past Year Questions (Topic-Wise)

The value of C, in Rolle's theorem for the function $f(x) = e^x \sin x$ , when $x \in [0, \pi]$ is :