Let $f$ be a twice differentiable function on $(1,6)$. If $f(2)=8, f^{\prime}(2)=5, f^{\prime}(x) \geq 1$ and $f^{\prime \prime}(x) \geq 4$, for all $x \in (1,6)$,...

The function $f(x)=\left\{\begin{array}{l}\frac{\pi}{4}+\tan ^{-1} x,|x| \leq 1 \\ \frac{1}{2}(|x|-1),|x|>1\end{array}\right.$ is :

Let $f:(0, \infty) \rightarrow(0, \infty)$ be a dif ferentiable function such that $f(1)=e$ and $\lim _{t \rightarrow x} \frac{t^2 f^2(x)-x^2 f^2(t)}{t-x}=0$ If $f(x)=1$, then $x$...

Let $K$ be the set of all real values of $x$ where the function $f(x)=\sin |x|-|x|+2(x-\pi)$ is not differentiable. Then the set K is equal...

Let $S$ be the set of points where the function, $f(x)=|2-|x-3| \|, x \in R$, is not differentiable. Then $\sum_{x \in S} f(f(x))$ is equal...

If the function $f(x)=\left\{\begin{array}{ll}a|\pi-x|+1, & x \leq 5 \\ b|x-\pi|+3, & x>5\end{array}\right.$ is continuous at $x=5$, then the value of $a-b$ is :

If the function $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}\frac{1}{x} \log _e\left(\frac{1+\frac{a}{x}}{1-\frac{x}{b}}\right) & , x<0 \\ k & , x=0 \\ \frac{\cos ^2 x-\sin ^2 x-1}{\sqrt{x^2+1}-1} & , x>0\end{array}\right.$
Is continuous...

Let $f:(-1,1) \rightarrow R$ be a function defined by $f(x)=\max \left\{-|x|,-\sqrt{1-x^2}\right\}$. If $K$ be the set of all points at which $f$ is not differentiable,...

The function $f(x)=\left|x^2-2 x-3\right| . e^{\left|9 x^2-12 x+4\right|}$ is not differentiable at exactly:

Let $a, b \in R, b \neq 0$, Define a function $...