1

I got this question for a finals review:enter image description here

The answer says it has no inflection point, but I got the second derivative to be

y''=2-2sinx

And when y''=0, x=2kπ+π/2

So how can this be?

Thanks.

P.S. The homework tag seems to be gone for some reason, so I can't add the tag.

Spongebob Squareroot-pants
  • 133
  • 1
    As another example, consider a line $y=ax+b$. Then in fact the second derivative is zero for all values of $x$, but of course there are no inflection points. – Théophile Dec 11 '15 at 03:34
  • 1
    This is a great opportunity to make use of test points. What happens immediately to the left/right of a zero of the second derivative? – The Chaz 2.0 Dec 11 '15 at 03:49

1 Answers1

4

Inflection point means the second derivative changes sign. This may or may not happen when the derivative is $0$. It doesn't happen here, the second derivative is always nonnegative.