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Math Help - Tangent Line

  1. #1
    compuryan
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    Exclamation Tangent Line

    if anybody could help with this that would be much appreciated:

    Find the point on the graph f(x)=4/3x^3 where the tangent line is perpendicular to the line y=-16x+3

    Thanks in advance

    -Ryan
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  2. #2
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    Quote Originally Posted by compuryan
    if anybody could help with this that would be much appreciated:

    Find the point on the graph f(x)=4/3x^3 where the tangent line is perpendicular to the line y=-16x+3

    Thanks in advance

    -Ryan
    Remember two lines are perpendicular to one another if and only if their slopes are negative reciprocals of each other.

    Thus, y=-16x+3 means the perpendicular line has slope 1/16.

    The slope of any given point on the graph f(x)=\frac{4}{3}x^3 is its derivative which is,
    f'(x)=4x^2.

    We need that to be 1/16 as explained in the first paragraph thus, 1/16=4x^2. Solving we have that x=\pm\frac{1}{8}. These are the two x-values on the graph where the tangent is perpendicular to this line.
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