Calculous
posted by Yoona on .
let f be the function defined by f(x)=12x^2/3 4X
a)find the intervals on which f is increasing
I got the rest of the question but I'm still not getting the increasing/decreasing thing

As we saw in a previous posting, f(x) is increasing where f'(x) is positive.
A positive slope means that when x increases, f(x) increases. A negative slope means that as x increases, f(x) decreases.
f'(x) = 8x^(1/3)  4
So, we want 8/x^1/3  4 > 0
8/x^1/3 > 4
1/x^1/3 > 1/2
x^1/3 > 2
x > 8 
Oops. Taking reciprocals reverses the direction of the inequality:
8/x^1/3  4 > 0
8/x^1/3 > 4
1/x^1/3 > 1/2
x^1/3 < 2
x < 8