We have the function f(x,y) = e^(-x^2 + y^2) :
a. To draw some level curves;
b. Calculate the gradient and determine the stationary points;
c. To write the equation of the tangent plane to z = f(x,y) in the point (0, 0, f(0, 0)), and in the point A (1,1,f(1,1));
d. To write the Taylor formula of f(x,y) stopped to the 2nd order, with center in the point (1,1);
e. Tell if the surface cross the tangent plane in A.
We solve several problems in mulitivariable calculus pertaining to a bell-shaped surface.