Consider the equation f(x,y) = −4x2+4x+y2+2y, the picture showssome of it’s level curves.
a. Completing the square, write the equations and identify thetraces f(x,y) = k for k = −1,0.
.(b) Draw the direction of fastest increase at the point (1,1)
.(c) Find the rate of change of f (x, y) = z at (1, 1) in thedirection of 〈−1, −2〉.
.(d) Â Â Find an equation for the tangent plane to thegraph of f at (1, 1, 3).
