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Math Help - Calculus Help

  1. #1
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    Calculus Help

    This question looks really simple and thats whats worrying me a liittle.

    Show that if f = f(x, y) and fyy=0, then f(x, y) = g(x)y + h(x) for some funcions g, h.

    I simply show that fyy​ = 0 by differnetiation. Is That it ?
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  2. #2
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    Re: Calculus Help

    \displaystyle \begin{align*} f_{yy} &= 0 \\ f_y &= \int{0\,dy} \\ f_y &= g(x) \textrm{ since partial differentiation of a function of x with respect to y gives 0} \\ f &= \int{g(x)\,dy} \\ f &= g(x)\,y + h(x) \end{align*}
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