Find the absolute extrema of f(x)=7x^{\frac{1}{3}}-x^{\frac{7}{3}} over the interval [-8,8].

Given:
Rectangular: A=200 $m^2$, length=x
Express the P as a function of x"

${\displaystyle f\left(x\right)=\{x^2+2,x\le 1.2x^2+2,x>1\}}$
a) f(-2) b) f(1)

Subsystem of infeasible system of linear inequalities
Suppose that we have a system of linear inequalities described by
$Ax\le b$
where $A$ is $m\times n$ matrix.
I want to show that if the system is infeasible then it has a subsystem of at most rank(A)+1 inequalities such that the subsystem is also infeasible.
My is initial thought was to use Farkas Lemma on the original system and modify the certificate y to obtain y′ as a certificate for a subsystem of at most rank(A)+1 inequalities, but I am stuck from there, maybe my initial thought it wrong?

Solve equations and inequalities
${\displaystyle 2x^2-11x-21=0}$
${\displaystyle x^2+x\ge 2}$

Linear systems of equations with 4 unknowns
$\begin{array}{rl}7& x+4y+3z+2w=46\\ 5& x-y+4w=23\\ & x+z=6\\ 3& x+7w=15\end{array}$

What is ${\displaystyle {(3+w+2w^2)}^4}$?
where w is cube roots of unity
We know that ${\displaystyle 1+w+w^2=0}$, so
${\displaystyle {(3-1-w^2+2w^2)}^4}$ or, ${\displaystyle {(2+w^2)}^4}$
How can I progress after this. Every suggestion will be appreciated.