Prove that the function are neither increasing nor decreasing :

$f\left(x\right)=x^2-x+1$ on $\left(-1, 1\right)$.

Prove that the function are neither increasing nor decreasing :

$f\left(x\right)=\frac{1}{x^2+1}$ on $\mathrm{R}$.

Find the interval in which the function are strictly increasing or strictly decreasing :

$f\left(x\right)=x^2-4x+6$.

Find the interval in which the function are strictly increasing or strictly decreasing :

$f\left(x\right)=x^2+2x-5$.

Find the interval in which the function are strictly increasing or strictly decreasing :

$f\left(x\right)=2x^2-3x$.

Find the interval in which the function are strictly increasing or strictly decreasing :

$f\left(x\right)=6-9x-x^2$.