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Math Help - Integral problem

  1. #1
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    Integral problem

    Find f(x) if f(1) = -1 and the tangent line at (x, f(x)) has slope 2e^x + 1

    This is a problem that was thrown into my indefinite integral homework, and I'm kinda stuck.

    any help appreciated.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by leviathanwave View Post
    Find f(x) if f(1) = -1 and the tangent line at (x, f(x)) has slope 2e^x + 1

    This is a problem that was thrown into my indefinite integral homework, and I'm kinda stuck.

    any help appreciated.
    the derivative gives the slope. thus if the slope at any x is 2e^x + 1 it means that:

    f'(x) = 2e^x + 1

    \Rightarrow f(x) = \int f'(x)~dx

    and use the fact that f(1) = -1 to solve for the arbitrary constant of integration
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