Find the maximum or minimum values, if any, without using derivatives, of the function:

$-(x-3{)}^2+9$

Find the maximum or minimum values, if any, without using derivatives, of the function:

$-\left|x+4\right|+6$

Find the maximum or minimum values, if any, without using derivatives, of the function:

$\sin \left(2x\right)+5$

Find the maximum or minimum values, if any, without using derivatives, of the function:

$\left|\sin 4x+3\right|$

Find the point of local maxima or local minima and the corresponding local maximum and minimum values of the following function:

$f\left(x\right)=(x-3{)}^4$

Find the point of local maximum or local minima and the corresponding local maximum and minimum values of the following function:

$f\left(x\right)=x^2$

Find the point of local maxima or local minima and the corresponding local maximum and minimum values of the following function:

$f\left(x\right)=2x^3-21x^2+36x-20$

Find the point of local maxima or local minima and the corresponding local maximum and minimum values of the following function:

$f\left(x\right)=x^3-6x^2+9x+15$

Find the point of local maxima or local minima and the corresponding local maximum and minimum values of the following function:

$f\left(x\right)=x^4-62x^2+120x+9$