# inflection points

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• Jul 27th 2008, 08:29 PM
zintore
inflection points
f(x)=x+sinx [0,2pi]
f'(x)=1 +cosx
f''(x)= -sinx
0=-sinx
x= 0, pi and 2pi
i dont know if i can call 0 and 2pi inflection points since they are end points of the closed interval....
• Jul 27th 2008, 08:37 PM
mr fantastic
Quote:

Originally Posted by zintore
f(x)=x+sinx [0,2pi]
f'(x)=1 +cosx
f''(x)= -sinx
0=-sinx
x= 0, pi and 2pi
i dont know if i can call 0 and 2pi inflection points since they are end points of the closed interval....

Critical points are found by solving f'(x) = 0, NOT f''(x) = 0.

Note also, that a point has coordinates, that is, an x-coordinate AND a y-coordinate.
• Jul 27th 2008, 08:38 PM
zintore
sorrry still not answered
but i was asking for the inflection points, where the graph changes concavity. can i say it changes concavity at an end point??
• Jul 27th 2008, 08:49 PM
TKHunny
1) The derivative does not exist at an endpoint.

2) Nothing can "change" at an endpoint, since there is only one side.

3) Extrema can occur at endpoints, but the calculus will find them only by design or coincidence. You must check the endpoints yourself.
• Jul 28th 2008, 07:47 AM
squarerootof2
i thought by definition inflection points are where f''(x)=0. is that not true?