The deflection $y(x)$ is given by

$y(x)=\frac{M}{6\text{E}\text{I}\text{L}}(x^3+3L{x}^2-4L^{2}x)$

$($a$)$ Determine the slope $(x)=\frac{dy}{dx}.$

$($b$)$ Determine both the location and value of the maximum deflection.

$($c$)$ Evaluate both the deflection and slope at the points $x=0$ and $x=L.$

$($d$)$ Use your results of parts $($b$)$ and $($c$)$ to sketch the deflection $y(x).$