# Math Help - concavity

1. ## concavity

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?

2. Originally Posted by DINOCALC09
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?

RonL

3. ok the second derivative is 2-5cox(x)

i graph it.

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?

4. i think that the answer is 2

anyone have any oppinoins?

5. Originally Posted by DINOCALC09
ok the second derivative is 2-5cox(x)

i graph it.

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 $[0,2 \pi]$, and as the second derivative is periodic with period $2 \pi$ in any of the intervals $[2 n \pi, 2 (n+1) \pi]$, and most closed intervals of length $2 \pi$ (the exeptions are intervals with a zero of $2-5 \cos(x)$ at an end point.

RonL