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Math Help - I need some help with a tangent line problem

  1. #1
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    I need some help with a tangent line problem

    Hi.

    I need some HW help again.

    Let f(x) = 12x + 15 - 13e^x . Then the equation of the tangent line to the graph of f(x) at the point (0, 2) is given by y=mx+b where:


    m = ?


    For f'(x), I get: 12 - 13e^x

    which I would think is the slope, but I can't get it to work out.

    Thanks
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  2. #2
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    Since you are already given the point (0,2) on the curve f(x), all you really need is to find m, and then plug in the point (0,2) and m into y = mx + b to solve for b. Notice that m = f'(0), and f'(0) = 12 - 13(e^0) = 12 - 13 = -1. Also note that  y = -x + b since m = -1. Plugging in 0 for x and 2 for y we see that  2 = -(0) + b , which means that  b = 2. This in turn means that  y = -1(x) + 2, and you are done!
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  3. #3
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    Wow. was that really all I had to do? plug in a 0 for the x? It all makes sense now but I was working on it forever and for some reason that never occurred to me.

    Anyway, thank you so much.
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