Question

Find the gradient of the function g(x,y)= xy at the point (5. - 1). Then sketch the gradient together with the level curve that passes through the point First find the gradient vector at (5. - 1). Vg(5. - 1)-01- i (Simplify your answers.) Choose the graph that shows the level curve and the gradient vector at (5. - 1). OD ОА.

Answer 1

This question is incomplete, the complete question is;

Find the gradient of the function g(x,y)= xy² at the point (5, - 1). Then sketch the gradient together with the level curve that passes through the point.

First find the gradient vector at (5, - 1).

Vg(5,- 1) = [ ]i - [ ]j (Simplify your answers.)

Choose the graph that shows the level curve and the gradient vector at (5, - 1).

options of the sketched graphs are uploaded along this answers

Answer:

Vg(5,- 1) = [ 1 ]i - [ 10 ]j

Option A is the correct graph for this Level

Step-by-step explanation:

Given that;

g(x,y) = xy²

we have to find gradient of this function at ( 5, -1 )

so

Δg(x,y) = dg/dx + dg/dy

d(g)/dx = y² ,       dg/dy = 2gx

therefore

Δg(x,y) = [y²]i + [2yx]j

Δ( 5, -1) = [-1²]i + [2×-1 ×5]j

=Δ(5, -1) = 1i - 10j

[ 1 ]i - [ 10 ]j

Therefore Option A is the correct graph for this Level