Page 711 Problem 5 Exercises 12.3

Evaluate \(f_x(x, y)\) and \(f_y(x, y)\) at the indicated point.

\(\color{red}{f(x, y) = x^2y-x+2y+3}\) at \(\color{red}{(1,2)}\)

\(f_x(x, y)\) = \(\frac{\partial(x^2y-x+2y+3)}{\partial x}\) \(\Rrightarrow\) \(2xy-1\)

\(f_x(1, 2)\) = \((2*1*2)-1\) \({\Rrightarrow}\) \(3\)

\(f_y(x, y)\) = \(\frac{\partial(x^2y-x+2y+3)}{\partial y}\) \(\Rrightarrow\) \(x^2+2\)

\(f_y(1, 2)\) = \(1^2+2\) \(\Rrightarrow\) \(3\)