Posted by Cam on .
Find the absolute maximum value and the absolute minimum value,
g(x)=1/8 x^2  4 x^(1/2) on [0, 9]

Calculus 
Reiny,
g'(x) = x/4  2x^(1/2) = x/4  2/√x
= 0 for a max/min
x/4 = 2/√x
x^(3/2) = 8
x = 8^(2/3) = 4
then f(4) = 2  4(2) = 6
for endpoints:
f(0) = 0
f(9) = 81/8  12 = 15/8 = 1.875
so within the given domain, the maximum function value is 0 , when x = 0