Find the absolute maximum and absolute minimum values of the function f(x)=x^3−12x^2−27x+8 over each of the indicated intervals.

Question

Find the absolute maximum and absolute minimum values of the function f(x)=x^3−12x^2−27x+8 over each of the indicated intervals.

(a) Interval = [−2,0].

1. Absolute maximum =

2. Absolute minimum =

(b) Interval = [1,10].

1. Absolute maximum =

2. Absolute minimum =

(c) Interval = [−2,10].

1. Absolute maximum =

2. Absolute minimum =

Answer 1

a) max 22, min 6

b) max -30, min -478

c) max 22, min -478

take the derivative and set it = 0. that gives x=9 as the min of -478, and x =-1 as the max of 22 if one isn't in the interval, check the end points.

x^2 -8x -9 =0

(x-9)(x+1) = 0

x=9, x=-1

f(9) = -478, f(-1) = 22

f(-2) = 6, f(1) =-30, f(10)= -462