Question

Calculate Gradient of P (x.y) at (x, y) = (1,2) and (2,1).

Answer 1

The gradient of P(x,y) can be calculated by taking the partial derivatives of P with respect to x and y. The gradient at (1,2) is (2, -4) and the gradient at (2,1) is (4, -2).

Step-by-step explanation:

The gradient of P(x,y) can be calculated by taking the partial derivatives of P with respect to x and y. Given the function P(x,y) = dx²-y², the partial derivative with respect to x is 2x and the partial derivative with respect to y is -2y.

To calculate the gradient at (1,2), substitute x=1 and y=2 into the partial derivatives. The gradient at (1,2) is (2(1), -2(2)) = (2, -4).

To calculate the gradient at (2,1), substitute x=2 and y=1 into the partial derivatives. The gradient at (2,1) is (2(2), -2(1)) = (4, -2).