Test Question 3 (5 points)
Given the surface $f(x,y) = \frac{x^2}{4} + 2\ln y$, and the point P = (-1, 3)
a -- 2 points) Find the rate of change of $f$ at P in the direction of v = (2, 9).
b -- 1 point) Find all direction vectors for which $f$ does not change at P (If there is more than one, describe them parametrically).
c -- 2 points) Provide the equation of a hypersurface G(x, y, z), for which the level surface G(x,y,z) = 0 is identical to the surface z = f(x,y), and find the normal to that level surface.
