6. Let f(x, y) = ln(2x - y²). (a) (b) (c) Determine the gradient of f at the point (2, -1). Determine the equation of the plane tangent to the graph of f at the point ( Find all unit vectors u such that Duf at (3, 2) is 0.

2. Consider the function f(x, y) = a) Find the directional derivative of f in the direction of the vector v (1,2) at the point (0,-2). b) Find a unit vector u in the direction in which f decreases most rapidly at the point (0,-2).

Find the directional derivative of the function at the given point in the direction of the vector v. f(x, у) 7e sin(y), (0, t/3), v = (-6, 8) Df(0, π/3) -

(1n |t – 1], e', vî ) 1. Let 7(t) = (a) Express the vector valued function in parametric form. (b) Find the domain of the function. (c) Find the first derivative of the function. (d) Find T(2). (e) Find the vector equation of the tangent line to the curve when t=2. 2. Complete all parts: (a) Find the equation of the curve of intersection of the surfaces y = x? and z = x3 (b) What is the name of the resulting curve of intersection? (c) Find the equation for B the unit binormal vector to the curve when t= 1. Hint: Instead of using the usual formula for B note that the unit binormal vector is orthogonal to 7 '(t) and 7"(t). In fact, an alternate formula for this vector is ア'(t) × ア"(t) ア(t) ×デ"(t)| B(t) =