Consider the following Textbook Problem:$-$

$5\mathrm{.}13$ Figure P$5\mathrm{.}13$a shows a uniform beam subject to a lin$-$

early increasing distributed load. The equation for the result$-$

ing elastic curve is $($see Fig. P$5\mathrm{.}13$b$)$

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

Use bisection to determine the point of maximum deflection

$($i$.$e$.,$ the value of $x$ where $d\frac{y}{d}x=0).$ Then substitute this

value into Eq$.($P$5\mathrm{.}13)$ to determine the value of the maximum

deflection. Use the following parameter values in your

computation: $L=600cm,E=50,000k\frac{N}{c}{m}^2,I=$

$30,000c{m}^4,$ and $w_0=2\mathrm{.}5k\frac{N}{c}m.$

Requirements:$-$

Use 'fplot' to visualize the function and estimate the locations of the roots.

Use Goal seek, solver, bisection, false position, secant methods $($using Excel$)$ to find the roots.

Compare these methods in terms of the number of iterations, accuracy, and speed $($if possible$)$

Summarize your findings and add your conclusions about the methods used.