Select ALL the intervals where f(x)= -x^3 + 3x^2 +1 is only decreasing. -infinity < x < 1 5 < x < infinity

Question

Select ALL the intervals where f(x)= -x^3 + 3x^2 +1 is only decreasing.

-infinity < x < 1
5 < x < infinity
-infinity < x < 0
-infinity < x < infinity
2 < x < infinity
0 < x < 2
1 < x < 5

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Ximena 1 week 2021-09-10T13:25:26+00:00 1 Answer 0

Answers ( )

    0
    2021-09-10T13:26:27+00:00

    Answer:

    5 < x < ∞

    -∞ < x < 0

    2 < x < ∞

    Step-by-step explanation:

    Given function is -x^{3} + 3x^{2} + 1.

    To, Calculate where the function is increasing or decreasing,

    we have to calculate the derivative of the function,

    so,

    f'(x) = -3x^{2} + 6x.

    Equating the f'(x)= 0 , we get

    x(-3x + 6) = 0

    So, f'(x) will be zero at x = 0 and x = 2.

    f(x) will be decreasing in the interval where f'(x) will be negative.

    now as the coefficient of f'(x) is negative it will be negative between

    the interval -∞ < x < 0 and 2 < x < ∞.

    Options which lie in these intervals only are

    5 < x < ∞

    -∞ < x < 0

    2 < x < ∞

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