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Math Help - 3rd degree equation and derivative

  1. #1
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    3rd degree equation and derivative

    f(x)=0.002x^3-0.08x^2+x
    Interval: 0 < x < 50

    I need to find the x-intervals, where the slope-angles are between 0 and 45 degrees with the x-axis' positive direction.

    I'm kinda lost?
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  2. #2
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    Quote Originally Posted by No Logic Sense View Post
    f(x)=0.002x^3-0.08x^2+x
    Interval: 0 < x < 50

    I need to find the x-intervals, where the slope-angles are between 0 and 45 degrees with the x-axis' positive direction.

    I'm kinda lost?
    1. Draw a graph of y = f(x)

    2. Find f'(x).

    3. Draw a graph of y = f'(x).

    4. Note that m = f'(x) = tan (theta) where theta is the angle between the x-axis's positive direction.

    5. Solve tan(0) < f'(x) < tan(45) <=> 0 < f'(x) < 1 (all angle sin degrees). The graph of y = f'(x) might help to see what's happening with this inequation.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    1. Draw a graph of y = f(x)

    2. Find f'(x).

    3. Draw a graph of y = f'(x).

    4. Note that m = f'(x) = tan (theta) where theta is the angle between the x-axis's positive direction.

    5. Solve tan(0) < f'(x) < tan(45) <=> 0 < f'(x) < 1 (all angle sin degrees). The graph of y = f'(x) might help to see what's happening with this inequation.
    I'm not sure I undertand number 4. Can you elaborate?
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  4. #4
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    Quote Originally Posted by No Logic Sense View Post
    I'm not sure I undertand number 4. Can you elaborate?
    m is the gradient of the tangent to the curve. It's given by f'(x).

    The tangent is a line. Have you met the formula m = tan theta, where theta is the angle between a line and the x-axis's positive direction?
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  5. #5
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    Alright, I understand now. Thank you.
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