Chapter 9.5, Problem 7E

Find the gradient of the function g(x,y) = xy at the point (5, 4). Then sketch the gradient together with the level curve that passes through the point. First find the gradient vector at (5, -4). Vg(5,-4)=i+ (Simplify your answers.)

Find the gradient of the function at the given point. Function Point f(x, у, 2) x² + y? + z? (2, 7, 4) = Vf(2, 7, 4) = Find the maximum value of the directional derivative at the given point.

Find the gradient of the function y = x³ + x² – 2x at points where - a. It crosses the x -axis b. It cuts the y -axis

Consider the following equation (151) f(x, у) - у/x, P(1, 3), 2i (a) Find the gradient of f. Vf(x, y) (b) Evaluate the gradient at the point P. Vf(1, 3) = (c) Find the rate of change of f at P in the direction of the vector u. Duf(1, 3)

Find the gradient of the function at the given point. Function Point f(x, у, 2) x² + y2 + z2 (8, 7, 3) %3D Vf(8, 7, 3) = %3D Find the maximum value of the directional derivative at the given point.

Find the gradient of the function g(x,y) = xy at the point (4, - 4). Then sketch the gradient together with the level curve that passes through the point. First find the gradient vector at (4, - 4). Vg(4, - 4) =i (Di (Simplify your answers.) li +

Find the gradient of the function at the given point. f(x, у) %3D 5х +Зу? + 5, (4, 1) Vf(4, 1) = %3D

a. What is the gradient at the point (4,0,1)?

Find the gradient of the function g(x,y) = xy2 at the point (4, - 4). Then sketch the gradient together with the level curve that passes through the point. First find the gradient vector at (4, - 4). Vg(4, - 4) = i + ( Di (Simplify your answers.) Choose the graph that shows the level curve and the gradient vector at (4, - 4). OA. O B. Oc. D. Ay