- #1
QuarkCharmer
- 1,051
- 3
Homework Statement
g(x) = 4x - tanx
Homework Equations
The Attempt at a Solution
[tex]g(\theta) = 4\theta - tan\theta[/tex]
[tex]g'(\theta)=4-sec^{2}\theta[/tex]
[tex]g'(\theta)=\frac{4cos^{2}\theta-1}{cos^{2}\theta}[/tex]
[tex]g'(\theta)=\frac{-4sin^{2}\theta}{cos^{2}\theta}[/tex]
[tex]-4tan^{2}\theta=0[/tex]
[tex]-4(tan\theta)(tan\theta)=0[/tex]
[tex]\theta = arctan0[/tex]
[tex]\theta = k\pi[/tex]
So, that lists the zeros of the derivative if I am correct. I believe the other critical points are pi/2 + kpi, where tan is undefined. That is all of the critical points correct?