Rolle's theorem is true for the function f(x) = x^2 - 4 in the in… - Vidyadip

MCQ

Rolle's theorem is true for the function $f(x) = {x^2} - 4 $ in the interval

A
$[-2, 0]$
✓
$[-2, 2]$
C
$\left[ {0,\,{1 \over 2}} \right]$
D
$[0,\,\,2]$

✓

Answer

Correct option: B.

$[-2, 2]$

b
(b) If Rolle's theorem is true for any function $f(x)$ in $[a,\,b].$

Then $f(a) = f(b),$ therefore $ [-2,2].$

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 STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The number of continuous functions $f :\left[0, \frac{3}{2}\right] \rightarrow(0, \infty)$ satisfying the equation $4 \int \limits_0^{3 / 2} f(x) d x+125 \int \limits_0^{3 / 2} \frac{d x}{\sqrt{f(x)+x^2}}=108$ is

If $\left[\begin{array}{cc}a+b & 2 \\ 5 & a b\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\end{array}\right]$, then find the values of $a$ and $b$ respectively.

The value of $\tan \left(2 \tan ^{-1}\left(\frac{3}{5}\right)+\sin ^{-1}\left(\frac{5}{13}\right)\right)$ is equal to:

If $\angle A = {90^o}$ in the triangle ABC, then ${\tan ^{ - 1}}\left( {\frac{c}{{a + b}}} \right) + {\tan ^{ - 1}}\left( {\frac{b}{{a + c}}} \right) = $

Let $ A$ be a $2$$ \times $$2$ matrix with non-zero entries and let ${A^2} = I$ where $I$ is $2\times 2$ identity matrix. Define $tr(A) =$ sum of diagonal elements of $A$ and $|A|=$ determinant of matrix $A$

Statement $-1 :$ ${\rm{tr}}\left( A \right) = 0$

Statement $-2 :$ $\det \left( A \right) = 1$

If $|A|=|k A|$, where $A$ is a square matrix of order 2 , then sum of all possible values of $k$ is

$2\cos^{-1}\text{x}=\sin^{-1}(2\text{x}\sqrt{1-\text{x}^2})$ is true for:

When a certain biased die is rolled, a particular face occurs with probability $\frac{1}{6}-\mathrm{x}$ and its opposite face occurs with probability $\frac{1}{6}+\mathrm{x}$. All other faces occur with probability $\frac{1}{6}$. Note that opposite faces sum to $7$ in any die. If $0\,<\,x\,<\,\frac{1}{6}$, and the probability of obtaining total $\mathrm{sum}=7$, when such a die is rolled twice, is $\frac{13}{96}$, then the value of $x$ is:

$\lim\limits_{x \rightarrow 0} \frac{\int\limits_{0}^{x} t \sin (10 t) d t}{x}$ is equal to

The differential equation $\frac{d^3y}{dx^3}-5y \frac{dy}{dx}+xy=0$ represents :-