The function $f(x) = |x - 1|$ is

A function f(x) is defined by $f(x)=\begin{cases}x^2+\alpha x+\beta: & 0\leq x<2\\3x+2 : & 2\leq x\leq4\\2\alpha x+5\beta :& 4<x\leq8\end{cases}$. If function f(x) is continuous on [0, 8], then value of $2\alpha+3\beta$ is

Observe the graph of a function $y = f(x)$ and identify the correct statements (s):

A. Function is continuous but not differentiable at $x = a$

B. Function is not defined at $x = a$

C. Function is defined at $x = a$ but not differentiable.

D. Given that at $x = a, y = b$.

Choose the correct answer from the options given below:

The greatest integer function $f(x) = [x]$ is differentiable for all values of

If $y^2 = ax + b, a,b \in \mathbb{R}$ where $\mathbb{R}$ is the set of real numbers, then $y\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2$ is equal to:

If $y = \log\left[\frac{x^2}{e^2}\right]$ then value of $\frac{d^2y}{dx^2}$ is :

If $\mathrm{e}^{\mathrm{y}}=\mathrm{x}^{\mathrm{x}}$, then which of the following is true ?