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Math Help - Gradient of a curve

  1. #1
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    Gradient of a curve

    Q:
    The gradient of a curve with equation y=f(x) is given by f1 (x) = x + sin2x.

    If f(0) = 1, find f(\pi )

    Any help would be appreciated
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  2. #2
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    If you're finding f(pi), just substitute x = pi and simplify...
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  3. #3
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    Quote Originally Posted by Prove It View Post
    If you're finding f(pi), just substitute x = pi and simplify...
    i think he is asking about f(pi) and not f1(pi) so u have to find f(x) by integrating the gradient and then just substitute f(0)=1 to find the value of the constant
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  4. #4
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    "f1" is not a standard notation for the ordinary derivative but you may indeed be right.
    Tim82, how about clarifying?
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  5. #5
    Senior Member Sambit's Avatar
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    Quote Originally Posted by islam View Post
    i think he is asking about f(pi) and not f1(pi) so u have to find f(x) by integrating the gradient and then just substitute f(0)=1 to find the value of the constant
    Exactly. So f(x)=\int x dx+\int \sin 2x dx=\frac{x^2}{2}-\frac{\cos 2x}{2}+c

    Putting f(0)=1 we have c=\frac{3}{2}

    So f(x)=\frac{x^2}{2}-\frac{\cos 2x}{2}+\frac{3}{2}

    So f(\pi)=\frac{{\pi}^2}{2}-\frac{\cos 2\pi}{2}+\frac{3}{2}=\frac{{\pi}^2}{2}-\frac{1}{2}+\frac{3}{2}=\frac{{\pi}^2}{2}+1
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