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Math Help - Equation of the line tangent to the curve

  1. #1
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    Equation of the line tangent to the curve

    I hope this is considered pre-calc...

    Here is the question:

    Suppose the line tangent to the graph of f at x=2 is y=5x+3 and suppose y=4x-1 is the line tangent to the graph of g at x=2. Find the line tangent to the following curves at x=2.

    y=f(x)g(x)

    I know the answer for the above is y=87x-83, but can someone show me the steps of the solution to come to that answer? I don't quite understand it. Thanks!
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  2. #2
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    Quote Originally Posted by softwareguy View Post
    I hope this is considered pre-calc...

    Here is the question:

    Suppose the line tangent to the graph of f at x=2 is y=5x+3 and suppose y=4x-1 is the line tangent to the graph of g at x=2. Find the line tangent to the following curves at x=2.

    y=f(x)g(x)

    I know the answer for the above is y=87x-83, but can someone show me the steps of the solution to come to that answer? I don't quite understand it. Thanks!
    y' = f'(x)g(x) + g'(x)f(x)

    y'(2) = f'(2)g(2) + g'(2)f(2) = slope of the tangent line to y = f(x)g(x) at x = 2

    point of tangency is (2, f(2)g(2))

    use the point-slope form to find the tangent line equation
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