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Expert: - 1/22/2008


Question
Hi Paul,
How many inflection points does the graph of y=sin(x)-1/3.sin(3x)-1/5.sin(5x) have on the interval 0<x<pi
note: the above is one third sin(3x) and one fifth sin(5x)
thanks much!
tell me when I need to find the number of inflection points I find f' set it to 0, get the critical points, then do I proceed to f'' just to get the behaviour or do i set f''=0 and solve... I am confused in this area

Answer
Questioner:   vince
Category:  Advanced Math
Private:  No
 
Subject:  inflection points
Question:  Hi Paul,
How many inflection points does the graph of y=sin(x)- (1/3)sin(3x)-(1/5)sin(5x) have on the interval 0<x<pi
note: the above is one third sin(3x) and one fifth sin(5x)
thanks much!
tell me when I need to find the number of inflection points I find f' set it to 0, get the critical points, then do I proceed to f'' just to get the behaviour or do i set f''=0 and solve... I am confused in this area

y' = cos x - cos 3x - cos 5x

y'' = - sin x + 3 sin 3x + 5 sin 5x


Another quick-and-dirty graph shows four zeroes, not counting the ones AT x = 0, x = pi.  I don't have anything better for you.

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