what are critical points for the function g(x)=36x-9tanx

Answer 1

Critical points are zeros, max,min,inflection.

zeros: g(x) = 0: lots of values, such as 0, 1.3, 4.7,... (eyeballing the graph)

max/min: g' = 0: 36 - 9sec^2 = 0
sec^2(x) = 4
sec(x) = 2
x = pi/3, 5pi/3, ...

inflection: g'' = 0: -18secx tanx = 0
where tanx = 0, or
odd multiples of pi/2

Answer 2

Hmmm. Also sec = -2