Consider the function f(x,y) = 8-(x+5)²-(y-3)²

To find the local extrema and saddle points, we first find critical points by checking where the first partial derivatives are each zero or undefined. Compute the first partial derivatives of f(x,y).

f_x(x,y) =

f_y(x,y) =

a.) What is the critical point?

b.)At the critical point you found, what is the value of f_xxf_yy-(f_xy)²?

c.) Is the critical point a local maximum, a local minimum, or a saddle point?