Question:

Given the function f$($x$)=$x$48$x$24$f$($x$)=$ x$^4-8$x$^2-4$:

a$)$ Find the local extreme values of the function using the first derivative test.

b$)$ Find the inflection points, if any, and determine the intervals of concavity.

c$)$ Sketch the graph of the function using the results from parts $($a$)$ and $($b$).$