consider S defined by

z = f(x,y) = x^2 + 4(y - 1)^2

1) Graph the level curves of f in the (x,y) plane. So will this be a 2D drawing, if/if not how do i do this? What will it look like?

2) Find/_\f{upside down triangle in front of'f'} and show where it is on graph.

so fx = 2x

fy = 8y - 8

3) Determine the directional derivative of'f'at (1, 1) in the direction of (1, 1).

so fx = 2x

fy = 8y - 8

sub in (1, 1) and i get (2, 0)

is directional vector 1/(1^2 + 1^2)= 1/2 ?

Where do i go from here?

4) Determine the maximum and minimum values of 'f'in the domain and show were the values occur on the graph.

{(x, y) | -1 <= x <= 1, 0 <= y <= 2}

Thank you, working would be much appreciated.