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Math Help - graph of derivative

  1. #1
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    graph of derivative

    The graph of a derivative f '(x) is shown in Figure 5.61.
    Figure 5.61. Graph of f', not f
    Fill in the table of values for f(x) given that f(0) = 5.

    x0123456f(x)5
    can someone get me started please...it would really help..thanks....
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  2. #2
    Senior Member Peritus's Avatar
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    we can see from the given graph that:

    f '(x) = -x_____0 <= x <= 1
    ______-1 _____1 <= x <= 3
    ______x-4_____3 <= x <= 5
    _______1______5 <= x <= 6

    let's integrate f '(x) in the first interval:

    f(x) = integ(-x dx) = -x^2 / 2 + C for all 0 <= x <= 1
    now we know that f(0) = 5, thus C = 5
    ---> f(x) = 5 - 0.5*x^2 0<= x <= 1
    which means that f(1) = 4.5

    now we proceed to integrate f '(x) in the following interval using the initial condition you've got from the previous interval namely f(1) = 4.5, we continue this way till the last interval...
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