Critical Numbers

Question

Find all critical numbers of of the function f (θ) = 2sec θ + tanθ, 14π < θ < 16π .

Answer 1

f (θ) = 2sec θ + tanθ

f' = 2sec θ tanθ + sec²θ = sec θ (2tan θ  + sec θ) = 0 at critical points.

The first factor is never 0.

Now we have to solve (2tan θ + sec θ) = 0 or 2 sin θ / cos θ + 1/cos θ = 0.

2 sin θ = -1   sin θ = -½.

 

θ = 14pi + 7pi/6  or  14pi + 11pi/6