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July 7th, 2017, 12:38 AM  #1 
Newbie Joined: Jun 2017 From: vancouver Posts: 3 Thanks: 0  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*(53x)(x)^(1/5), (52x)(x)^(1/5), 1/3*(25x)(x)^(1/3) , 1/2*(35x)(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*(25x)(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 02:22 AM. 
July 7th, 2017, 02:34 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,164 Thanks: 1423 
You identified f'(x) correctly. Try giving the critical numbers as 0 and 2/5 (without the parentheses).


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curve, decreasing, increasing or, sketching 
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