Question

If f(x, y) = xy, find the gradient vector ∇f(2, 5) and use it to find the tangent line to the level curve f(x, y) = 10 at the point (2, 5). gradient vector tangent line equation Sketch the level curve, the tangent line, and the gradient vector.

Answer 1

Answer:

Step-by-step explanation:

check attachment

f(x,y)=xy       Δf(2,5)

fx=y = 5

fy=x = 2

Gradient Vector:

<5,2>

Tangent Vector:

0=fx(x-2) + fy(y-5)

0=5(x-3) + 2(y-2)

11=5x+2y