You are given the exponential revenue function $R(p)=500p*e^{-0\mathrm{.}04p}.$ Please perform the following five tasks:

a$)$ Determine the derivative $R^{\text{'}}(p)$

b$)$ Determine the critical point of $R(p)($there should be just one$)$

c$)$ Classify the critical point using the First Derivative Test. You must use the proper format and include all appropriate components of the test.

d$)$ Classify the critisal point using the Second Derivative Test. You must use the proper format and include all appropriate components of the test.

e$)$ Perform the Extreme Value Theorem on the interval $[0,80],$ You must use the proper format and include all appropriate components of the test.