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.