1. The problem statement, all variables and given/known data 1.if the derivative of f(x,y) with respect to x and y both exist, then f is differentiable at (a,b) 2. if (2,1) is a critical point of f and fxx (2,1)* fyy (2,1) < (fxy (2,1))^2, then f has a saddle point at (1,2) 3. if f(x,y) has two local maxima, then f must have a local minimun 4. Dk f(x,y,z)= fz (x,y,z) 2. Relevant equations 3. The attempt at a solution 1. i think it is right, but i can't come up with a good explanation 2. i think it is right according to the second derivative test, but for some reason, the wording of this question keeps making me think this question is wrong 3. i thnk it is right, because if f( x,y) has 2 local max, then there must be a local min between those two local max because the graph must decrease after the first local max 4. i have no idea, can someone explain? can someone tell me what i did is right or nor?