HW$3\_7$ Optimization problem

The deflection of a uniform beam subject to a linearly increasing distributed load can be computed as

$y=\frac{w_0}{120\text{E}\text{I}\text{L}}(-x^5+2L^2{x}^3-L^{4}x)$

Given that $L=600cm,E=50,000\frac{kN}{c{m}^2},I=30,000c{m}^4$ and $w_0=2\mathrm{.}5\frac{kN}{cm},$

determine the point of maximum deflection by using an appropriate built$-$in function. Finally plot the deflection with respect to $x$ and mark the point of maximum deflection with a green dot. Also print the value of the maximum deflection on the screen with a print statement.

Note:

The maximum of function $f(x)$ happens at $\frac{df}{dx}=0$

The range of the plot should be dictated by the length of the beam. Python code only