(1 point) If f (x, y) = 1x2 + 2y2 , find the value of the directional derivative at the point (2, 4) in the direction given by the angle 6 = 25\". \f(1 point) Find the gradient of the function f(x, y, z) = y In(zx), at the point (e, 2, 1) Vf(e, 2, 1) =(1 point) If the gradient of f is V f = 23; x? + 4yzi and the point P = (1, 7, 2) lies on the level surface f (x, y, z) = 0, find an equation for the tangent plane to the surface at the point P. Z: (1 point) Consider the function f(x, y) = (ex x) 00801). Suppose S is the surface 2 = f(x, y). (3) Find a vector which is perpendicular to the level curve of f through the point (2, 5) in the direction in which f decreases most rapidly. vector = (b) Suppose 1-5 = 1? + 1; + ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (2, 5). What is a? a