Help Please!
Find the global extreme values of the function f on the given interval and where they occur.
f(x)=x^(2/3)*(x-5)^2 on the interval [0,2].

Question

Help Please!
Find the global extreme values of the function f on the given interval and where they occur.
f(x)=x^(2/3)*(x-5)^2 on the interval [0,2].

amistre64 · Answer

test the end points, then find your critical values of the derivative to test

anonymous · Answer

I got $$f \prime (x)= 2(x-5)x ^{2/3} + \frac{ 2(x+5)^2 }{ 3x^{1/3} }$$
I equaled that to zero and got $$x=5 $$ and $$x=\frac{ 5 }{ 4 }$$
then I pluged the values in and got f(0)=0 , f(5)=0 and f(5/4)=69.42.....
@amistre64 

I'm guessing my mins are at f(0) and f(5)? and my max at f(5/4)
But how would I prove my point?