# How do you find the critical numbers of #g(θ) = 4 θ - tan(θ)#?

##### 1 Answer

#### Explanation:

Extrema

or

That is

for

and

for

graph{4x-tan(x) [-7, 7, -7, 7]}

graph{sin(x)/cos(x)^3 [-7, 7, -30, 30]}

As you can see on the bottom plot, and as expected, the second derivative of g changes sign at x = 0. Therefore x=0 is an inflection point. The extrema are true extrema. The second derivative does not change sign at the extrema. If it did, these would not be extrema but saddle points.