(a) Compute the derivative of the function F(x, Y, z) = x² + 2y² – 3z? at the point (1,1, 1) in the direction of v =i+j+k. %D (b) Let f(x,y, z) = xz sin(y). Compute the limit f(1+h, T – h,-1) – f(1,7, –1) -1) – f(1, 7, –1) lim h→0 h

2. For the function z = f(x, y) is known f (2, – 1) = -2, f-(2, -1)=-1, f,(2, –1) = 2. Find the following (a) Gradient of f at the point (2, –1) :grad f(2, -1) (b) Directional derivative of f at the point (2, – 1) in the direction of the vector –27+37: fa(2, –1 ). (c) Estimate f(1.99, –1.02) = (d) Differential of f at the point (2, -1)

2. Consider the function f: R²R such that f(x, y) = x²y-2xy² +6xy-3y² +18y +4. (a) Show that f has precisely two stationary points: (-4,-1), and (0,3). (b) Determine the nature of these two stationary points.