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Math Help - calculus help - finding equation of a tangent line

  1. #1
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    Cool calculus help - finding equation of a tangent line

    prob:

    Given that f(3)=-1 and f derivative(3)=5, find an equation for the tangent line to the graph of y=f(x) at x=3

    the answer is y=5x-16 , but i dont know how to get there :/
    any help is much appreciated!
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  2. #2
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    Well the derivative is defined as the slope of the tangent line, so if you use slope-intercept notation of y=mx+b, then

    you already know : y=5x + b for the tangent line.

    Because the tangent line is at x=3, then a point on the tangent line is also at x=3. The problem gives you f(3)= -1 so there is a tangent line at (3,-1).

    Plug those values into the equation to get b: -1=5(3) + b.
    So, -1= 15 + b ........... -16=b!!

    So the final equation is y=5x -16.

    Glad I could use my calc knowledge somewhere! you can thank me later.....
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  3. #3
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    Smile

    thank you
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