Finding the point of inflection for the function

1. The problem statement, all variables and given/known data

Find any points of inflection for the function y = x - cos x on the interval {0,2pi}

2. Relevant equations



3. The attempt at a solution

Well i know the second derivative is cos x, and I know it equals 0. But im just not sure what to give as a final answer. cos x = 0 at pi/2 and 3pi/2 but is that the final answer?

Thank you for your help!
 
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1. The problem statement, all variables and given/known data

Find any points of inflection for the function y = x - cos x on the interval {0,2pi}

2. Relevant equations



3. The attempt at a solution

Well i know the second derivative is cos x, and I know it equals 0. But im just not sure what to give as a final answer. cos x = 0 at pi/2 and 3pi/2 but is that the final answer?

Thank you for your help!
cos(x) is not identically zero. To confirm that there are inflection points for x = pi/2 and x = 3pi/2, check to see whether the concavity changes around these values. IOW, does y'' change sign at pi/2 and 3pi/2? If so, you're almost done, and the only other thing is to find the y values at these points. Those will be your inflection points.
 
how do I check around those values, Im not sure how to use something like pi/2 in this case.
 

HallsofIvy

Science Advisor
41,626
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Then use pi/2+ .001 and pi/ - .001! What do you mean "use pi/2"? It is a number! enter it into your calculator. Be sure you calculator is set to "radian" mode of course.
 

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