Three Curve Analysis Questions

[BayernBlues]

Here are a few curve analysis questions that I'm having problems with. For the 3rd one where it says fully analyze, it means: Find intervals of increase/decrease, concavity, points of inflection, symmetry, and graph. I'm having problems with the symmetry and sketching part although I think that I did the other stuff wrong too for that question.

http://img412.imageshack.us/img412/2336/6711tj4.png

Here's my attempt at the solution:

http://img339.imageshack.us/img339/8564/xo2my2.png

*Could someone move this to the calculus homework thread. It's questions for test prep, not homework but I guess it'd go under that section of the site.

 

[HallsofIvy]

It's not clear to me what you are doing with the first problem. To find the slope of the tangent line, of course, you need to find the derivative of y, but I see no indication of y' in what you wrote. One problem I see is determining the correct value of y for x= -1.

For the second problem, you've done okay except that you say there is no maximum. The is no "global" maximum but there are local maxima. With the information you have, it should be easy to draw a rough sketch of the graph.

For the third problem f' is never 0 and f is not defined when f' is not defined so there are no critical points. An "inflection" point is where f' changes sign which can only happen where f"= 0 (or where it is not defined but that only happens where f itself is not defined