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Math Help - checking the tangent line

  1. #1
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    checking the tangent line

    How does one check if the tangent line to a curve is correct with out graphing technology.

    For example, y = (2x^2 + 5)(x - 3)^2, when x = 2 the tangent line is y = -18x+49.

    How do I know that this is true?
    Last edited by Barthayn; May 25th 2011 at 12:14 PM.
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  2. #2
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    e^(i*pi)'s Avatar
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    When x=2 the tangent line will be a number rather than an equation.

    The derivative is defined as the tangent line of a function at any given point so if you correctly take the derivative (here use the chain rule and product rule) you will have an equation for the tangent line.

    Given your equation I seriously doubt the tangent is -18x+49 since your original function is 5th order so I'd expect a derivative of 4th order.
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  3. #3
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    Quote Originally Posted by e^(i*pi) View Post
    When x=2 the tangent line will be a number rather than an equation.

    The derivative is defined as the tangent line of a function at any given point so if you correctly take the derivative (here use the chain rule and product rule) you will have an equation for the tangent line.

    Given your equation I seriously doubt the tangent is -18x+49 since your original function is 5th order so I'd expect a derivative of 4th order.
    tangent line is always linear.
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  4. #4
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    Quote Originally Posted by Barthayn View Post
    tangent line is always linear.
    The slope at x=2 is -18.
    Your tangent line is correct.
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  5. #5
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    Quote Originally Posted by Barthayn View Post
    How does one check if the tangent line to a curve is correct with out graphing technology.

    For example, y = (2x^2 + 5)(x - 3)^3, when x = 2 the tangent line is y = -18x+49.

    How do I know that this is true?
    It's not true, look it up in some type of graphing software.
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  6. #6
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    Quote Originally Posted by scounged View Post
    It's not true, look it up in some type of graphing software.
    It was suppose to be to the two, not three. I mistyped.
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