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Math Help - Find the equation of line tangent

  1. #1
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    Find the equation of line tangent

    Find the equation of the line tangent to the graph of f at (2, 7), where f is given by f(x) = 2x^3 - 9x^2 + 3.

    I'm confused. Step by step if at all possible.
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  2. #2
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    Quote Originally Posted by Latszer View Post
    Find the equation of the line tangent to the graph of f at (2, 7), where f is given by f(x) = 2x^3 - 9x^2 + 3.

    I'm confused. Step by step if at all possible.
    Equation of tangent: y - 7 = m(x - 2) where m = f'(x) evaluated at x = 2.
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    Quote Originally Posted by Latszer View Post
    Find the equation of the line tangent to the graph of f at (2, 7), where f is given by f(x) = 2x^3 - 9x^2 + 3.

    I'm confused. Step by step if at all possible.
    1) Find the derivative of f(x)
    f(x)=2x^3-9x^2+3
    f'(x)=6x^2-18x

    2) Plug in x (2) to the derivative to find the slope.
    m=6(2)^2-18(2)
    m=6(4)-36
    m=24-36
    m=-12

    3) Use y-y1=m(x-x1) to find the slope of the tangent line
    y=7, x=2, m=-12
    y-7=-12(x-2) You can finish here, or distribute if you want.
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