SOLUTION: Find the global maximum and minimum for the function on the closed interval. 18x^1/3 -6x on the interval -1 less or equal to x less or equal to 8 Enter the exact answers. En

Algebra ->  Equations -> SOLUTION: Find the global maximum and minimum for the function on the closed interval. 18x^1/3 -6x on the interval -1 less or equal to x less or equal to 8 Enter the exact answers. En      Log On


   



Question 1069395: Find the global maximum and minimum for the function on the closed interval.
18x^1/3 -6x
on the interval -1 less or equal to x less or equal to 8
Enter the exact answers. Enter the values for x in increasing order.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Graphing,
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Using calculus,
y=18x%5E%281%2F3%29-6x
dy%2Fdx=6%2Fx%5E%282%2F3%29-6
Setting the derivative to zero,
6%2Fx%5E%282%2F3%29-6=0
6%2Fx%5E%282%2F3%29=6
x%5E%282%2F3%29=1
x=1
Since the second derivative is negative, when x=1, this value is a maximum.
Find the minimum value by checking the endpoints.
f%28-1%29=-18%2B6=-12
f%288%29=36-48=-12