Question
what are critical points for the function g(x)=36x-9tanx
Answers
Steve
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
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
Steve
Hmmm. Also sec = -2