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!
The point of inflection for a function is the point where the concavity of the function changes. It is the point where the function transitions from being concave up to concave down or vice versa.
To find the point of inflection for a function, you must first find the second derivative of the function. Then, set the second derivative equal to zero and solve for the variable. The resulting value will be the x-coordinate of the point of inflection.
Yes, a function can have multiple points of inflection. This occurs when the concavity of the function changes multiple times within the domain.
The point of inflection can tell us about the behavior of the function. It marks the transition from increasing to decreasing or vice versa and can also indicate the presence of local maximum or minimum points.
Yes, the point of inflection can also be found graphically by observing the shape of the graph. The point of inflection will be the point where the curve of the graph changes from concave up to concave down or vice versa.