# need help on inflection and critical points!

• Dec 7th 2008, 11:03 AM
rodgers44
need help on inflection and critical points!
i was wondering if anyone could look at these problems, they're all due Monday night and I can't seem to find close enough relations to the problems in my book to get any answers. Any help would be really appreciated.

http://img519.imageshack.us/img519/2937/allpagesku9.jpg
• Dec 7th 2008, 11:23 AM
Mentia
I think in general,

points of inflection occur where there is a concavity change, which means the 2nd derivative passes through zero.

critical points occur where the first derivative is zero or infinity/undefined

So for instance, on #1, take two derivatives with respect to x and then set it equal to zero and use the quadratic formula to solve for x.

For two variables, to find critical points you take an x derivative of the original function, and then a y derivative of the original function, and set both those derivatives to zero and solve for x and y (you have 2 equations with 2 unknowns).