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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.

          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.

Test Question 3 (5 points)
Given the surface f(x,y) = (x^2)/(4) + 2ln 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.

Added by John H.

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