# Find the function given partial derivatives and points

Find $$f(x,y)$$ given $$f_x= 3x^2y-4y^2$$ and $$f_y=x^3-8xy+6y$$ and $$f(1,1)=5$$

Can anyone steer me in the right direction here? I assume I have to integrate but we haven't done integration with multivariable functions yet. Any help at all is appreciated.

Integrate with respect to $$x$$ and $$y$$ your partial derivatives. In both cases, you'll get a constant term which in this case is a function of y or x respectively.
For example $$\int f_x dx = x^3y-4xy^2+c(y)$$
Do the same for $$f_y$$ and set them equal and solve.
• Alternatively, differentiate $x^3 y - 4xy^2 + c(y)$ partially with respect to $y$ (not forgetting the the $c'(y)$ term), set equal to $x^3 - 8xy + 6y$, and solve for $c'(y)$. – Theo Bendit Oct 22 '18 at 0:21