009A Sample Final 1, Problem 10

Consider the following continuous function:

$f(x)=x^{1/3}(x-8)$

defined on the closed, bounded interval $[-8,8]$.

a) Find all the critical points for $f(x)$.

b) Determine the absolute maximum and absolute minimum values for $f(x)$ on the interval $[-8,8]$.

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Step 3:

Final Answer:
(a)
(b)

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