If f(x)=e^ x in [0, ], then c in Rolle's theorem is: 1. 6 2. 4 3. 2 4. 3 4

4. 3 4 Solution: f(x)=e^ x f'(x)=e^ x +e^ x f'(c)=0 e^c( + )=0 + =0 =- =-1 c=3 4 (0, )

If f(x)=e^ x in [0, ], then c in Rolle's theorem is: 1. 6 2. 4 3.…

Download App

Question

If $\text{f}(\text{x})=\text{e}^{\text{x}}\sin\text{x}$ in $[0,\pi],$ then c in Rolle's theorem is:

$\frac{\pi}{6}$
$\frac{\pi}{4}$
$\frac{\pi}{2}$
$\frac{3\pi}{4}$

✓

Answer

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

Solution:
$\text{f}(\text{x})=\text{e}^{\text{x}}\sin\text{x}$
$\text{f}'(\text{x})=\text{e}^{\text{x}}\cos\text{x}+\text{e}^{\text{x}}\sin\text{x}$
$\text{f}'(\text{c})=0$
$\text{e}^\text{c}(\cos\text{c}+\sin\text{c})=0$
$\cos\text{c}+\sin\text{c}=0$
$\cos\text{c}=-\sin\text{c}$
$\tan\text{c}=-1$
$\text{c}=\frac{3\pi}{4}\in(0,\pi)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Mean Value Theorems→Mean Value Theorems — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.

	Number of cars manufactured
Colour	Vento	Creta	WagonR
Red	65	88	93
White	54	42	80
Black	66	52	88
Sliver	37	49	74

What was the total number of black cars manufactured?

→

The domain of function $\cos ^{-1}(2 x-3)$ is :

→

The probability distribution of a discrete random variable $X$ is given below:

$\text{X}:$	$1$	$2$	$3$	$4$
$\text{P}(\text{X}):$	$\frac{1}{10}$	$\frac{1}{5}$	$\frac{3}{10}$	$\frac{2}{5}$

The value of $E(X^2)$ is:

→

The value of $\int\limits^\frac{\pi}{2}_0\log\Big(\frac{4+3\sin\text{x}}{4+3\cos\text{x}}\Big)\text{dx}$ is:

2
$\frac{3}{4}$
0
-2

→

Which of the following statements is correct?

Every LPP admits an optimal solution
A LPP admits unique optimal solution
If a LPP admits two optimal solution it has an infinite number of optimal solutions
The set of all feasible solutions of a LPP is not a converse set

→

If the events $A$ and $B$ are mutually disjoint then the value of $P(A \cap B)$ is

→

If $\text{f(x)}=\text{x}\sin\frac{1}{\text{x}},\text{ x}\neq0,$ then the value of the function at x = 0, so that the function is continuous at x = 0, is: