Q55 / 150 · MHT CET 2016 · Mathematics

If Rolle's theorem for a function $f (x) = e^{x} (\sin x - \cos x)$ is verified on $[\frac{π}{4}, \frac{5 π}{4}]$ then the value of $c$ is

A
$\frac{π}{3}$
B
$\frac{π}{2}$
C
$\frac{3 π}{4}$
Correct answer
D
$π$

Solution

Given,

f (x) = e^{x} (\sin x - \cos x)

∴ f^{'} (x) = e^{x} [\cos x + \sin x] + [\sin x - \cos x] e^{x}

∴ f^{'} (x) = 2 e^{x} \sin x

To verify Rolle's Theorem.

f^{'} (c) = 0

2 e^{c} \sin c = 0

\Rightarrow \sin c = 0

∴ c = π

Hence, the correct answer is option: 'D'.

Relevant Questions

The function satisfies all the conditions of Rolle's theorem in , then20 Apr, 2026 (E)Mean Value Theorem
The value of satisfied by the Rolle's theorem for the function , is...19 Apr, 2026 (M)Mean Value Theorem
Rolle's theorem holds for monic quadratic polynomial on the interval where . Similarly, also follows Rolle's theorem in the interval where ,19 Apr, 2026 (E)Mean Value Theorem
If the function satisfies all the conditions of Rolle's theorem on and the slope of the tangent to the curve at is zero, then18 Apr, 2026 (E)Mean Value Theorem
If the function satisfies Roll's theorem in , if then is equal to...15 Apr, 2026 (M)Mean Value Theorem
Let be the differentiable function for all such that and . The maximum value of is...13 Apr, 2026 (E)Mean Value Theorem