- #1
QuarkCharmer
- 1,051
- 3
Homework Statement
I am doing the various ins and outs of curve sketching and the mean value theorem and all that jazz with this function:
[tex]f(x)=sec(x)+tan(x)[/tex]
Homework Equations
The Attempt at a Solution
I took the first derivative to be:
[tex]f'(x)=sec(x)tan(x)+sec^{2}(x)[/tex]
I am having trouble finding the inflection points with the second derivative.
I took the second derivative to be:
[tex](sec(x)tan(x))tan(x)+sec(x)(sec^{2}(x))+2sec(x)(sec(x)tan(x))[/tex]
I simplified to: (left out the x's for brevity)
[tex]sectan^{2}+sec^{3}+2sec^{2}tan[/tex]
[tex]sec(sec^{2}-1)+sec^{3}+2sec^{2}tan[/tex]
[tex]sec^{3}-sec+sec^{3}+2sec^{2}tan[/tex]
[tex]2sec^{3}-sec+2sec^{2}tan=0[/tex]
Trying to solve this set to zero for the second derivative test and I have no idea how to go about it without using a calculator so far. I have not been able to simplify it into something that I can solve?
I was thinking that maybe I could square both sides (including the zero) and then use the pythag identity to convert that last tangent into a secant, and then maybe I would have a polynomial that I could use PQ test to solve or something (but idk if that is ok to do, seems reasonable to me). Any pointers?