Question

Given the following function in two variables x and y

f(x, y) = x³y + 2x⁴ + y⁵

a. Find the Jacobean determinant at points P (3,2)

b. Find the Hessian determinant at points P (1,3)

Answer 1

$f'_x=3x^2y+8x^3,$

$f'_y=x^3+5y^4,$

$f''_x=6xy+24x^2,$

$f''_y=20y^3,$

$f''_{xy}=3x^2.$