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Math Help - Help with a calculus test question

  1. #1
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    Help with a calculus test question

    I need to redo this question to get partial credit but it looks like none of the examples or homework we've done:

    Given f'(x) = 4e^(2x) and  f(0) = 1, find the function f(x)?
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  2. #2
    Super Member PaulRS's Avatar
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    Let's see it this way, if you have f(x)=C\cdot{x^2}+k where C and k are real numbers, derivating: f'(x)=C\cdot{2}\cdot{x}

    Then C\cdot{x^2}+k is the anti-derivative of C\cdot{2}\cdot{x}

    That's denoted as follows: \int{C\cdot{2}\cdot{x}}\cdot{dx}=C\cdot{x^2}+k

    To find the anti-derivative you need (there are an infinit number of them) you have to find the constant k, and for that you use the other information you have

    Read here:
    http://www.mathhelpforum.com/math-he...66-post12.html

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  3. #3
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    Quote Originally Posted by PaulRS View Post
    Let's see it this way, if you have f(x)=C\cdot{x^2}+k where C and k are real numbers, derivating: f'(x)=C\cdot{2}\cdot{x}

    Then C\cdot{x^2}+k is the anti-derivative of C\cdot{2}\cdot{x}

    That's denoted as follows: \int{C\cdot{2}\cdot{x}}\cdot{dx}=C\cdot{x^2}+k

    To find the constant k you use the other information you have

    Read here:
    http://www.mathhelpforum.com/math-he...66-post12.html

    this seems to work but i don't think we've gone over anti-derivatives yet. so far this section we've only gone over implicit differentiation, related rates, increments, linear approximation, increasing and dec functions, mean value theorem, and the first derivative test.
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  4. #4
    Super Member PaulRS's Avatar
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    Oh sorry, I didn't realised it was f(x)=4\cdot{e^{2x}} that you wanted.
    Be careful when writing the exponent f(x)=4\cdot{e^{2x}}

    Well, for this case given y=C\cdot{e^{2x}}+k derivating we have: y'=2\cdot{C}\cdot{e^{2x}} where C and k are real numbers
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