Question

Given f(x_(1), x_(2)) = x_(1)^(1/2) x_(2)^(1/2), if H is the Hessian matrix, then |H|.

Answer 1

The Hessian matrix calculates the second-order partial derivatives of a function. For the given function f(x1, x2) = √(x1)√(x2), the Hessian matrix can be calculated by finding the second-order partial derivatives.

Step-by-step explanation:

The Hessian matrix is a square matrix of second-order partial derivatives of a function. In this case, the function f(x1, x2) = √(x1)√(x2). To find the Hessian matrix, we need to calculate the second-order partial derivatives of f with respect to x1 and x2.

The Hessian matrix, H, is given by:

H = | ∂2f/∂x12 ∂2f/∂x1∂x2 |

| ∂2f/∂x2∂x1 ∂2f/∂x22 |