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Math Help - Find Max Value Based on F' Graph

  1. #1
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    Find Max Value Based on F' Graph



    The graph of f', the derivative of the function f, is shown above for x on the closed interval of [0,10]. The areas of the regions between the graph of f' and the x-axis are 20, 6, and 4, respectively. If f(0)=2, what is the maximum value of f on the closed interval [0,10]?

    a. 16
    b. 20
    c. 22
    d. 30
    e. 32

    I have no clue how to solve this one.
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  2. #2
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    Quote Originally Posted by summermagic View Post


    The graph of f', the derivative of the function f, is shown above for x on the closed interval of [0,10]. The areas of the regions between the graph of f' and the x-axis are 20, 6, and 4, respectively. If f(0)=2, what is the maximum value of f on the closed interval [0,10]?

    a. 16
    b. 20
    c. 22
    d. 30
    e. 32
    f has maximums where f' changes sign from positive to negative and at the right endpoint, x = 10.

    let the first x-intercept > 0 be a

    f(a) = 2 + \int_0^a f'(x) \, dx = 2 + 20 = 22

    f(10) = 2 + \int_0^{10} f'(x) \, dx = 2 + 18 = 20

    maximum value of f(x) on the interval [0, 10] should now be clear.
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