Find the intervals on which the function f(x)=x²/³(10-x) is increasing and decreasing. Sketch the graph of y=f(x)and identify any local maxima and minima. Any global extrema should also be identified.

Answer 1

y = x^(2/3)(10-x) = 10x^(2/3) - x^(5/3)
y' = (20/3)x^(-1/3) - (5/3)x^(2/3)
= 5/3 (4-x)/x^(1/3)

y'=0 when x=4

y increases when y'>0, or x<4

see the graph and info at

http://www.wolframalpha.com/input/?i=x^%282%2F3%29%2810-x%29