You are given the exponential revenue function $\backslash ($ R$($p$)=400$ p $\backslash$cdot e$^\{-0\mathrm{.}025$ p$\}\backslash ).$ Please perform the following five tasks: a$)$ Determine the derivative $\backslash ($ R$^\{\backslash$prime$\}($p$)\backslash )$ b$)$ Determine the critical point of $\backslash ($ R$($p$)\backslash )($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 critical 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 $[0,100],$ You must use the proper format and include all appropriate components of the test.