Question

Find ∂h/∂x and ∂h/∂y for h(x, y) = 2x + 3y^2 - 6. Identify the set of points at which h is continuous. Option 1: ∂h/∂x = 2, ∂h/∂y = 6y; Continuous everywhere Option 2: ∂h/∂x = 2, ∂h/∂y = 6y; Continuous only at y = 0 Option 3: ∂h/∂x = 2, ∂h/∂y = 6; Continuous everywhere Option 4: ∂h/∂x = 2, ∂h/∂y = 3y; Continuous only at y = 0

Answer 1

Hi,

answer: option 2

Explanation:

`h(x,y)=2x+3y^2-6\\\\\frac{\partial{dh}}{\partial{x}} =2\\\\\frac{\partial{dh}}{\partial{y}} =3*2y=6y\\\\`

`\text{ h(x,y) is continuous everywhere }`