MAC 2313 Midterm: MAC2313 F99 Test 2

Directional Derivative: Problem 3 Previous Problem List Next (1 point) Consider the function f(x, y) -5xy2-x3y. Find the gradient off: Find the gradient of f at the point (2, -4). Find the rate of change of the function f at the point (2, -4) in the direction u = 〈-1/11, V120/11).

5. (15 pts) Find the directional derivative of the function f(x, y) e cos(xy) at the point (2, 0) in the direction of the vector v 3i -4j

2. Let f(x, y) =xy + . x (a) Find Vf(xy) and Vf(-1,1) ▽f(x,y)= Vf(-1,1 (b) Give the Cartesian equation of the tangent plane to the graph of f at the point where x =-1,y= 1. (c) Find the directional derivative of f at (-1,1) in the direction of the vector(-3,1) (d) In which direction will f decrease most rapidly at (-1,1)? Give the rate of decrease in this direction.