In [0, 1] Lagrange's mean value theorem is NOT applicable to - Vidyadip

MCQ

In $[0, 1]$ Lagrange's mean value theorem is $ NOT$ applicable to

✓
$f(x) = \left\{ {\begin{array}{*{20}{c}}
{\frac{1}{2} - x,\,\,\,\,\,\,\,\,\,x < \frac{1}{2}} \\
{{{\left( {\frac{1}{2} - x} \right)}^2},\,x \geqslant \frac{1}{2}}
\end{array}} \right.$
B
$f(x) = \left\{ {\begin{array}{*{20}{c}}
{\frac{{\sin x}}{x}\,\,x \ne 0} \\
{1,\,\,\,\,\,\,\,\,x = \frac{1}{2}}
\end{array}} \right.$
C
$f(x) = x|x|$
D
$f(x) = |x|$

✓

Answer

Correct option: A.

$f(x) = \left\{ {\begin{array}{*{20}{c}}
{\frac{1}{2} - x,\,\,\,\,\,\,\,\,\,x < \frac{1}{2}} \\
{{{\left( {\frac{1}{2} - x} \right)}^2},\,x \geqslant \frac{1}{2}}
\end{array}} \right.$

a
(a) The function defined in option $ (a) $ is not differentiable at $x = \frac{1}{2}$.

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 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The area of the region formed by $\text{x}^2+\text{y}^2-6\text{x}-4\text{y}+12\leq0,\text{ y}\leq\text{x}$ and $\text{x}\leq\frac{5}{2}$

$\frac{\pi}{6}-\frac{\sqrt{3}+1}{8}$
$\frac{\pi}{6}+\frac{\sqrt{3}+1}{8}$
$\frac{\pi}{6}-\frac{\sqrt{3}-1}{8}$
none of these

Choose the correct answer from the given four options.
Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability, that both cards are queens, is:

Given $ABC$ is an equilateral triangle of side length $1$ unit and $P$ be any arbitrary point on the circumcircle of triangle $ABC,$ then $|\vec PA|^2+|\vec PB|^2+|\vec PC|^2$ is equal to

Let $f:[0, \infty) \rightarrow R$ be a continuous function such that $f(x)=1-2 x+\int_0^x e^{x-t} f(t) d t$ for all $x \in[0, \infty)$. Then, which of the following statement (s) is (are) $TRUE$?

$(A)$ The curve $y=f(x)$ passes through the point $(1,2)$

$(B)$ The curve $y=f(x)$ passes through the point $(2,-1)$

$(C)$ The area of the region $\left\{(x, y) \in[0,1] \times R: f(x) \leq y \leq \sqrt{1-x^2}\right\}$ is $\frac{\pi-2}{4}$

$(D)$ The area of the region $\left\{(x, y) \in[0,1] \times R: f(x) \leq y \leq \sqrt{1-x^2}\right\}$ is $\frac{\pi-1}{4}$

Let $y=y(x)$ be the solution curve of the differential equation secy $\frac{d y}{d x}+2 x \sin y=x^3 \cos y$, $y(1)=0$. Then $y(\sqrt{3})$ is equal to :

Let $D _{ k }=\left|\begin{array}{ccc}1 & 2 k & 2 k -1 \\ n & n ^2+ n +2 & n ^2 \\ n & n ^2+ n & n ^2+ n +2\end{array}\right|$. If $\sum \limits_{ k =1}^n$ $D _{ k }=96$, then $n$ is equal to

The value of a for which the function $\text{f(x)}=\begin{cases}5\text{x}-4,&\text{if }0<\text{x}\leq1\\4\text{x}^2+3\text{ax},&\text{if }<\text{x}<2\end{cases}$ is continuous at every point of its domain, is:

$\frac{13}{3}$
1
0
-1

The order the matrix is $\begin{bmatrix}2&\text{amp; }3&\text{amp; }4\\9&\text{amp; }8&\text{amp; }7\end{bmatrix}$ is:

4 × 3
3 × 2
2 × 3
3 × 1

The function $f(x) = \;|px - q|\; + r|x|,\;x \in ( - \infty ,\;\infty )$, where $p > 0,\;q > 0,\;r > 0$ assumes its minimum value only at one point, if

Let $[ x ]$ be the greatest integer $\leq x$. Then the number of points in the interval $(-2,1)$, where the function $f(x)=|[x]|+\sqrt{x-[x]}$ is discontinuous is $........$.