Condition for Strictly Decreasing

Q.

The graphical representation of x > 2 on number line is

1. 

2. 

3. 

4. 

Q. How many equation are there of a circle in complex number form?

Q. Let $f$ be a twice differentiable function in $(-\infty ,\infty )$ such that $f^{\prime \prime }\left(x\right)\le 0\forall x\in R.$ If $g\left(x\right)=f\left(x\right)+f(1-x)$ and $g^{\prime }\left(\frac{1}{4}\right)=0,$ then

1. $g\left(x\right)$ is increasing in $(-\infty ,0)$
2. $g\left(x\right)$ attains local minimum at $x=\frac{1}{2}$
3. $g^{\prime \prime }\left(x\right)=0$ has at least two roots in $[0,1]$
4. $g^{\prime }\left(x\right)<0$ for all $x\in (\frac{1}{2},\infty )$

Q. All the functions with straight line graphs are either strictly increasing functions or strictly decreasing functions.

1. F