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July 6th, 2017, 11:38 PM   #1
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Curve Sketching: Increasing/ Decreasing

For f(x)=x^(2/3)−x^(5/3) find the critical numbers and open intervals where the function is increasing and decreasing.

Since f'(x)=(?), choose from
1/5*(5-3x)(x)^(-1/5),
(5-2x)(x)^(-1/5),
1/3*(2-5x)(x)^(-1/3) ,
1/2*(3-5x)(x)^(-1/3) ,
we see that f'(x)=0 if x=(?) and that f'(?) does not exist.
Therefore, the critical numbers are (?) and (?)

My answers is f'(x)=1/3*(2-5x)(x)^(-1/3)
f'(x)=0 if x=2/5 and that f'(0) does not exist
Therefore, the critical numbers are (0) and (2/5),
but it's not correct and I'm not sure what's wrong.

Last edited by skipjack; July 7th, 2017 at 01:22 AM.
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July 7th, 2017, 01:34 AM   #2
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You identified f'(x) correctly. Try giving the critical numbers as 0 and 2/5 (without the parentheses).
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