009A Sample Final 3, Problem 9

Let

$g(x)=(2x^{2}-8x)^{\frac {2}{3}}$

(a) Find all critical points of  $g$  over the  $x$-interval  $[0,8].$

(b) Find absolute maximum and absolute minimum of  $g$  over  $[0,8].$

Foundations:
1. To find the critical points for  $f(x),$  we set  $f'(x)=0$  and solve for  $x.$
Also, we include the values of  $x$  where  $f'(x)$  is undefined.
2. To find the absolute maximum and minimum of  $f(x)$  on an interval  $[a,b],$
we need to compare the  $y$  values of our critical points with  $f(a)$  and  $f(b).$

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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