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

  • slu -

    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

  • slu -

    Hmmm. Also sec = -2

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