If n is a positive integer, how many times does the function f(x) = x^2 + 5cos(x) change concavity in the interval 0 is less than or equal to x which is less than or equal to 2*pi*n?
If n is a positive integer, how many times does the function f(x) = x^2 + 5cos(x) change concavity in the interval 0 is less than or equal to x which is less than or equal to 2*pi*n?
This is asking: How many times does f''(x) change sign in the interval [0, 2*n*pi].
and see that in between every 2pi it changes sign twice, so that means that the answer is it changes n-times as the answer?
It changes concavity twice in the interval , and as the second derivative is periodic with period in any of the intervals , and most closed intervals of length (the exeptions are intervals with a zero of at an end point.