(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is part of a problem for a nonlinear diff class... But it's the basic stuff that's tripping me up.

Find all the max/min and concavity for

[tex]v(x) = -cos(x)-Lx+1,\ \ \ 0<L<1 [/tex]

3. The attempt at a solution

Here's what I do:

[tex] v'(x) = sin(x)-L [/tex]

[tex]v''(x)=cos(x)[/tex]

Set the first derivative to 0:

[tex]sin(x)-L=0 \Rightarrow x = arcsin(L)[/tex]

Here's where I'm confused. I say

[tex]x = arcsin(L) + 2\pi n, \ \ \ \mbox{where }n \mbox{ is any integer}[/tex]

But Maple says:

[tex]x = arcsin(L)+2\pi n, \ \ \ \mbox{where }n \mbox{ is any integer, OR:}[/tex]

[tex]x = arcsin(L) - 2arcsin(L)+2\pi n+\pi \ \ \ \mbox{where }n \mbox{ is any integer}[/tex]

Where does the -2arcsin(L) and the +pi come from?????

I really want to understand this once and for all.... I never took a trig class, and while I get by fine 99% of the time, I hit a brick wall when I come across this kind of stuff.

Thanks!

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# Homework Help: Strange Trig Function solutions

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