My Math Forum Curve Sketching: Increasing/ Decreasing

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 July 6th, 2017, 11:38 PM #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*(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.
 July 7th, 2017, 01:34 AM #2 Global Moderator   Joined: Dec 2006 Posts: 17,919 Thanks: 1386 You identified f'(x) correctly. Try giving the critical numbers as 0 and 2/5 (without the parentheses).

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