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.