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Math Help - Find the Tangent Line Equation

  1. #1
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    Find the Tangent Line Equation

    I need some help with these problems:

    Find an equation of the tangent line to the curve at the given point:

    1. y = (x-1)/(x-2), (3,2)

    2.y = 2x^3-5x, (-1,3)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dm10 View Post
    I need some help with these problems:

    Find an equation of the tangent line to the curve at the given point:

    1. y = (x-1)/(x-2), (3,2)

    2.y = 2x^3-5x, (-1,3)
    do you know how to find the equation of a line if you are given the slope and a point the line passes through?

    note that the derivative gives you the formula for the slope at any value of x
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    do you know how to find the equation of a line if you are given the slope and a point the line passes through?

    note that the derivative gives you the formula for the slope at any value of x
    I don't know what to do.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dm10 View Post
    I don't know what to do.
    for the first, apply the product rule: \frac d{dx} \frac {f(x)}{g(x)} = \frac {f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}

    once you find the derivative, plug in x = 3. that will give you the slope of the line, that is, m, in y = mx + b. now you know m and you know (x,y) = (3,2) you can find b and hence the equation of the line.

    do a similar thing for the second problem, except when finding the derivative, use the power rule which i told you about in your other post

    try it
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  5. #5
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    Quote Originally Posted by Jhevon View Post
    for the first, apply the product rule: \frac d{dx} \frac {f(x)}{g(x)} = \frac {f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}

    once you find the derivative, plug in x = 3. that will give you the slope of the line, that is, m, in y = mx + b. now you know m and you know (x,y) = (3,2) you can find b and hence the equation of the line.

    do a similar thing for the second problem, except when finding the derivative, use the power rule which i told you about in your other post

    try it
    I do that but I keep getting the wrong answer.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dm10 View Post
    I do that but I keep getting the wrong answer.
    show your work, i can tell you where you are messing up
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  7. #7
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    y-y_1=m(x-x_1) Your slope is the answer to the x value plugged in your derivative. The x value is the value plugged into your original equation, the y is the value of that.
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