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Math Help - Find the intervals INC/DEC

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    Find the intervals INC/DEC

    For the function f(x) find the intervals on which it is inc/dec.

    f(x)= x⁴ - 4x + 10
    f'(x) = 4x - 12x or 4x(x - 3) => x=3

    so i have the intervals (-∞, 3) and (3, ∞) i'm using the test values 1 and 4 and im plugging my test values into f'(x).

    I'm getting -8 for the test value 1 so its decreasing, and 64 for the test value 4 so it's increasing.

    DEC on (-∞, 3) and INC on (3, ∞).

    My professor got INC on (-∞ , 3) ; DEC on (3, ∞) can you spot what i'm doing wrong?
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  2. #2
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    Quote Originally Posted by Johnny Walker Black View Post
    For the function f(x) find the intervals on which it is inc/dec.

    f(x)= x⁴ - 4x + 10
    f'(x) = 4x - 12x or 4x(x - 3) => x=3

    so i have the intervals (-∞, 3) and (3, ∞) i'm using the test values 1 and 4 and im plugging my test values into f'(x).

    I'm getting -8 for the test value 1 so its decreasing, and 64 for the test value 4 so it's increasing.

    DEC on (-∞, 3) and INC on (3, ∞).

    My professor got INC on (-∞ , 3) ; DEC on (3, ∞) can you spot what i'm doing wrong?
    I do not agree w/ your professor.

    f'(x) = 4x^2(x-3) = 0

    critical values of x are x = 0 and x = 3

    the factor 4x^2 > 0 for all x \ne 0

    x-3 < 0 for all x < 3 ... f(x) is decreasing

    x-3 > 0 for all x > 3 ... f(x) is increasing

    graph attached.
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