Question

Find the absolute maximum and absolute minimum values of the function

f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals.
Enter -1000 for any absolute extrema that does not exist.

(A) Interval = [1,4]
Absolute maximum =

Absolute minimum =

(B) Interval = [1,8] .
Absolute maximum =

Absolute minimum =

(C) Interval = [4,9] .
Absolute maximum =

Absolute minimum =

My answers are:
(A) Interval = [1,4]
Absolute maximum = 9

Absolute minimum = -5

(B) Interval = [1,8] .
Absolute maximum = 173

Absolute minimum = -5

(C) Interval = [4,9] .
Absolute maximum = 459

Absolute minimum = -1000

Only the max for the second one and the max for the third one are right.... I don't know what to do....

Answer 1

f'(x)=(x-5)^3+(x-2)3(x-5)^2=(4x-11)(x-5)^2
(A) Absmax=f(1)=64+11=75
Absmin=f(11/4)=-3^7/2^8+11=-2187/256+
+11=629/256
(B) Absmax=f(8)=173
Absmin=f(11/4)=629/256
(C) Absmax=f(9)=459
Absmin=f(4)=9