93
MCQ (Single Correct Answer)
The derivative of $\cos ^{-1}\left(2 x^2-1\right)$ w.r.t. $\cos ^{-1} x$ is
A
2
B
$\frac{-1}{2 \sqrt{1-x^2}}$
C
$\frac{2}{x}$
D
$1-x^2$
94
MCQ (Single Correct Answer)
If $x=t^2$ and $y=t^3$, then $\frac{d^2 y}{d x^2}$ is equal to
A
$\frac{3}{2}$
B
$\frac{3}{4 t}$
C
$\frac{3}{2 t}$
D
$\frac{3}{2 t}$
95
MCQ (Single Correct Answer)
The value of $c$ in Rolle's theorem for the function $f(x)=x^3-3 x$ in the interval $[0, \sqrt{3}]$ is
A
$1$
B
$-1$
C
$\frac{3}{2}$
D
$\frac{1}{3}$
96
MCQ (Single Correct Answer)
For the function $f(x)=x+\frac{1}{x}, x \in[1,3]$, the value of $c$ for mean value theorem is
A
1
B
$\sqrt3$
C
2
D
None of these
97
An example of a function which is continuous everywhere but fails to be differentiable exactly at two points is ............. .
Explanation
$|x|+|x-1|$ is continuous everywhere but fails to be differentiable exactly at two points $x=0$ and $x=1$.
So, there can be more such examples of functions.