Graphical Interpretation of Derivative

Q.
The derivative of the curve

1. Will be same at all the points
2. Will be positive at all points
3. Will be negative at all points
4. Will be positive at some points and negative at some points and zero at some

Q. The function $f\left(x\right)={\sin }^{-1}\left(\cos x\right)$ is

1. continuous at x = 0.
2. not continuous at x = 0.
3. differentiable at x = 0.
4. not differentiable at x = 0.

Q. The set of all points, where the function $f\left(x\right)=\frac{x}{1+\left|x\right|}$ is differentiable is

1. $\left(-\infty ,\infty \right)$
2. $[0,\infty )$
3. $\left(-\infty ,0\right)\cup \left(0,\infty \right)$
4. $\left(0,\infty \right)$

Q. Number of point(s) where the function $f\left(x\right)=max(\sqrt{2x-x^2},2-x)$ is non-differentiable, is/are

1. \N
2. 1
3. 2
4. 3