Which of the following function can satisfy Rolle's theorem ? - Vidyadip

MCQ

Which of the following function can satisfy Rolle's theorem ?

A
$f(x) = |\ sgn\ (x)|$ in $[-1, 1]$ (where $sgn\ (x)$ represents signum function)
B
$f(x) = 3x^2 - 2$ in $[2, 3]$
C
$f(x) = |x - 1|$ in $[0, 2]$
✓
$f(x) = (x + \frac{1}{x})$ in $[\frac{1}{3} , 3]$

✓

Answer

Correct option: D.

$f(x) = (x + \frac{1}{x})$ in $[\frac{1}{3} , 3]$

d

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

If $\int_{}^{} {\frac{{2x + 3}}{{{x^2} - 5x + 6}}} \;dx = 9\;\ln (x - 3) - 7\ln (x - 2) + A$, then $A = $

Let $\mathrm{F}:[3,5] \rightarrow \mathrm{R}$ be a twice differentiable function on $(3,5)$ such that $\mathrm{F}(\mathrm{x})=\mathrm{e}^{-\mathrm{x}}$ $\int_{3}^{x}\left(3 t^{2}+2 t+4 F^{\prime}(t)\right) \,d t$

If $F^{\prime}(4)=\frac{\alpha e^{\beta}-224}{\left(e^{\beta}-4\right)^{2}}$, then $\alpha+\beta$ is equal to $....$

A sphere of radius 100mm shrinks troximate decreo radius 98mm, then the appase in its volume is:

If magnitudes of vectors $\vec a,\vec b,\,\vec c$ are $3, 4,$ and $5$ respectively $\vec a\,$ and $\,\vec b + \,\vec c,\, \vec b\,$ and $\,\vec c + \,\vec a,$ $\vec c\,$ and $ \,\vec a + \,\vec b,$ perpendicular to each other, then $\left| {\vec a + \vec b + \vec c} \right|=$

Let $f: R \rightarrow R$ be a function defined as $f(x)=a \sin \left(\frac{\pi[x]}{2}\right)+[2-x], a \in R$, where [t] is the greatest integer less than or equal to $t$. If $\lim _{x \rightarrow-1} f(x)$ exists, then the value of $\int_{0}^{4} f(x) d x$ is equal to.

Let $f:[0,2] \rightarrow R$ be a function which is continuous on $[0,2]$ and is differentiable on $(0,2)$ with $f(0)=1$.

Let $F(x)=\int_0^{x^2} f(\sqrt{t}) d t$ for $x \in[0,2]$. If $F^{\prime}(x)=f^{\prime}(x)$ for all $x \in(0,2)$, then $F(2)$ equals

The distinct linear functions that map $[-1, 1]$ onto $[0, 2]$ are:

What is the order of the product $-\begin{bmatrix}\text{x}&\text{amp;}\text{ y}&\text{amp;}\text{ z}\end{bmatrix}\begin{bmatrix}\text{a} &\text{amp;}\text{ h}&\text{amp;}\text{ g} \\\text{h} &\text{amp;}\text{ b}&\text{amp; }\text{f}\\\text{g} &\text{amp;}\text{ f}&\text{amp; }\text{c} \end{bmatrix}\begin{bmatrix}\text{x}\\\text{y}\\\text{z}\end{bmatrix}$ is:

Area bounded by the curve $y = \log x\,,$ $x - $ axis and the ordinates $x = 1,\,\,x = 2$ is

If $\text{A}=\begin{bmatrix}\alpha &\text{amp; 2} \\2 &\text{amp; }\alpha \end{bmatrix}$and $ |\text{A}^3|=125,$ then $\alpha$ is equal to: