The discussion revolves around finding points of inflection for the function y = x - cos x on the interval {0, 2pi}. Participants are exploring the implications of the second derivative, which is identified as cos x, and its behavior at specific points.
Some participants have provided guidance on checking for changes in concavity around the identified points of pi/2 and 3pi/2, suggesting specific numerical values to test. However, there is still uncertainty regarding the final answer and the method of verification.
Participants are working within the constraints of a homework assignment, focusing on the interval {0, 2pi} and the requirement to determine points of inflection without providing complete solutions.
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 said: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!