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Math Help - slope of tangent line

  1. #1
    helpme
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    slope of tangent line

    can someone explain to me on how to do this problem?
    the slope of the tangent line to the curve y = 4sqrt(x) at point (7,10.5831) is:___
    The equation of this tangent line can be written in the form y = mx+b where m is:___ and b is:___
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by helpme View Post
    can someone explain to me on how to do this problem?
    Code:
    the slope of the tangent line to the curve
    y = 4sqrt(x)  at point (7,10.5831) is:___ 
     
    The equation of this tangent line can be written in
    the form  y = mx+b where m is:___ and b is:___
    The slope of the tangent line at the point is the same thing as the
    gradient of the curve at that point. You find the gradient by taking
    the derivative of the equation of the curve, so:

    dy/dx=4* 1/2 * 1/sqrt(x)

    (note I am using "*" as the multiplication symbol here, which is a common
    convention when writting maths in plain ASCII)

    At the point in question x=7, so the gradient is:

    dy/dx = 2/sqrt(7)~=0.75593.

    Now we know the slope of the line we can write the equation of the
    line in the form:

    y=0.75593*x+b.

    but we also know that this line is a tangent to the curve at (7,10.5831),
    so we know that:

    10.5831=0.75593*7+b.

    Which can be solved for b to give the full equation of the desired line.

    RonL
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