Posted by **Yoona** on Sunday, November 20, 2011 at 4:33pm.

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

- Calculous -
**Steve**, Sunday, November 20, 2011 at 10:25pm
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

- Calculus - Correction -
**Steve**, Sunday, November 20, 2011 at 10:27pm
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

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