Consider the function f(x, y,z) = 3x2 + 5 y ~ 7x22 . a) Suppose we were to pass through the point (1,1,1) with unit speed in a direction parallel to the vector (1, 2, 2) . At what rate would the values of this function be changing at that moment? That is, what would be the directional derivative of f at the given point and in the given direction? b) Consider the level surface dened by the equation 3x2 + 5 y 7x222 = l . Find an equation for a plane tangent to this surface at the point (1,1,1)