Already factored, nice
So all we have to do is set each factor equal to zero
x^(4/5) = 0 ----> x = 0 , f(0) = 0
(x-1)^2 = 0 ----> x = 1 , f(1) = 0
F ' (x) = x^(4/5) (2(x-1)) + (4/5)x^(-1/5) (x-1)^2
= (2/5)x^(-1/5) (x-1) [5x + 2(x-1)]
= (2/5)(x-1)(7x-2)/x^(1/5
= 0 for max/mins
x = 1 or x = 7/2
A quick sketch in Wolfram will show how these affect the graph
http://www.wolframalpha.com/input/?i=F%28x%29%3Dx%5E%284%2F5%29%28x-1%29%5E2
find the critical numbers of the function
F(x)=x^(4/5)(x-1)^2
1 answer