2. Optimization Problems
Solve and plot the following expressions using python. Plot a red dot at your solution.
- Find all roots of this expression:
$$
\frac{(x−4)^4}{8}+ \frac{(x−2)^2}{2} - 4
$$
- Find the minimum of this expression with $r$ bounded to be $[0.9,3]$
$$
4\left[\frac{1}{r^8} - \frac{1}{r^4}\right]
$$
Solve $e^{x / 4} = x$
You do not need to plot this problem. Solve the following system of equations and report your answer.
$$
2\sqrt{x} - 3 \cos z = 3
$$$$
2 x - z^2 = 18
$$