# Does the second derivative test tell you anything about inflection points?

I am confused by two sources of information. Wikipedia tells me that the second derivative test cannot be used to determine inflection points. However, on the Harvey Mudd calculus page, it says that you can:

"If f'(c) exists and f''(c) changes sign at x=c, then the point (c,f(c)) is an inflection point of the graph of f. If f''(c) exists at the inflection point, then f''(c)=0"

http://www.math.hmc.edu/calculus/tutorials/secondderiv/

My book doesn't mention anything about it, but I learned from my instructor that you could use the second derivative test to find inflection points. Could anyone clear up this disagreement in calculus?

Think about the shape of the curve $y = \sin x$ at the origin. Draw the curve and its tangent there, and observe the sign of the second derivative near the origin.