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