SOLUTION: Find the absolute maximum and minimum of the function
{{{ f(x)= x^(1/3)*(x^2-9)}}} for x∈[-4,2]
Express your answers in simple exact form.
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Question 592124: Find the absolute maximum and minimum of the function
for x∈[-4,2]
Express your answers in simple exact form.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
I'll expand everything in order to avoid using the product rule.
 = x^{\frac{7}{3}} - 9x^{\frac{1}{3}})
 = \frac{7}{3}x^{\frac{4}{3}} - 9(\frac{1}{3})x^{-\frac{2}{3}} = \frac{7}{3}x^{\frac{4}{3}} - 3x^{-\frac{2}{3}})
Set to zero and find all possible values of x (remember to check them). Also, check the endpoints x = -4 and x = 2, as the min/max could occur there.
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