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Math Help - Graphing

  1. #1
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    Graphing

    Consider the equation below.
    f(x) = 2(cos(x))2 - 4sin(x)
    0 ≤ x ≤ 2
    (a) Find the interval on which f is increasing.
    (b) Find the local minimum and maximum values of f.
    (min)
    (max)

    (c) Find the inflection points. (Order your answers from smallest to largest x-value.)
    ( , ) (smaller x value)
    ( , ) (larger x value)

    Find the interval on which f is concave up.
    Find the intervals on which f is concave down.
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  2. #2
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    Quote Originally Posted by sheva2291 View Post
    Consider the equation below.
    f(x) = 2(cos(x))2 - 4sin(x)
    0 ≤ x ≤ 2
    (a) Find the interval on which f is increasing.
    (b) Find the local minimum and maximum values of f.
    (min)
    (max)

    (c) Find the inflection points. (Order your answers from smallest to largest x-value.)
    ( , ) (smaller x value)
    ( , ) (larger x value)

    Find the interval on which f is concave up.
    Find the intervals on which f is concave down.
    set f'(x) = 0 to find critical values in the given interval

    find the sign of f'(x) between critical values to whether f(x) is increasing or decreasing

    set f''(x) = 0 to find critical values in the given interval

    find the sign of f''(x) between critical values to whether f(x) is concave up or down ... inflection points occur where concavity changes.
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