Finding the point of inflection for the function

[meeklobraca]

Homework Statement

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

Homework Equations

The Attempt at a Solution

Well i know the second derivative is cos x, and I know it equals 0. But I am 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!

 

[Mark44]

Homework Statement

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

Homework Equations

The Attempt at a Solution

Well i know the second derivative is cos x, and I know it equals 0. But I am 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.

 

[meeklobraca]

how do I check around those values, I am not sure how to use something like pi/2 in this case.

 

[HallsofIvy]

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.