SOLUTION: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x^3 − 18x^2 − 54x + 1, [−2, 4]

Algebra ->  Equations -> SOLUTION: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x^3 − 18x^2 − 54x + 1, [−2, 4]      Log On


   

Question 1086873: Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = 6x^3 − 18x^2 − 54x + 1,
[−2, 4]
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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Take the derivative and set it equal to each other to find extrema,
df%2Fdx=18x%5E2-36x-54
18x%5E2-36x-54=0
x%5E2-2x-3=0
%28x-3%29%28x%2B1%29=0
Two solutions:
x-3=0
x=3
and
x%2B1=0
x=-1
Take the second derivative to find which is which,
d2f%2Fdx2=2x-2
At x=-1, 2x-2=2%28-1%29-2=-4 so the maximum occurs here.
At x=3,2x-2=2%283%29-2=4 so the minimum occurs here.