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Math Help - Finding the inc/dec of the function thru critical number.....

  1. #1
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    Finding the inc/dec of the function thru critical number.....

    Find inc/dec interval of the following function:

    f(x) = x^4-50x^2+4

    My work:

    f'(x) = 4x^3-100x

    4x^3-100x = 0
    4x(x^2-25) = 0
    4x = 0 ----> x= 0
    x^2-25 = 0----> x = 5, x = -5

    So, (-5,0,5) are the critical point....

    I cannot find the increasing and decreasing intervals, because when I substittue critical points in f(x) to positive or negative, it just give me negative value.

    Can you plz help me by giving me the correct answer.

    Thx
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Detroit, MI
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    Quote Originally Posted by kashifzaidi View Post
    Find inc/dec interval of the following function:

    f(x) = x^4-50x^2+4

    My work:

    f'(x) = 4x^3-100x

    4x^3-100x = 0
    4x(x^2-25) = 0
    4x = 0 ----> x= 0
    x^2-25 = 0----> x = 5, x = -5

    So, (-5,0,5) are the critical point....

    I cannot find the increasing and decreasing intervals, because when I substittue critical points in f(x) to positive or negative, it just give me negative value.

    Can you plz help me by giving me the correct answer.

    Thx
    Did you evaluate f'(x) at some test values within each of the implied intervals?
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  3. #3
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    There are no intervals.

    I just need to find where the graph is increasing or decreasing
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Detroit, MI
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    Quote Originally Posted by kashifzaidi View Post
    There are no intervals.

    I just need to find where the graph is increasing or decreasing
    Yes! there are intervals, they're just implied!

    When you find those critical values, you are locating the place where where the tangent line to f(x) will be horizontal, but you have THREE places where it is horizontal. -5, 5, and 0, so, in these intervals, you must determine whether or not f'(x) (the slope of f(x)) is negative or positive. If it's negative, the function is decreasing, if it's positive the function is decreasing.

    So, the intervals are

    (-\infty,-5),(-5,0),(0,5),and(5,\infty) . Choose an arbitrary # in each one of these intervals and evaluate the slope of f(x)!
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