Let f be the piecewise–defined function
f(x)={x2+4x+5,20−2x,0≤x≤3,3<x≤8.
The domain of f is the closed interval [0,8].
(a) For each piece, compute f′(x). Identify every value of x in (0,8) at which f′(x)=0.
(b) Create a complete list of all candidates for absolute extreme values of f on [0,8]. Briefly explain why no other points need to be considered.
(c) Evaluate f at every candidate found in part (b) and at both endpoints of the domain.
(d) State the absolute maximum and absolute minimum values of f on [0,8], including the x–coordinates at which they occur.