function of two variables is given by f(x, y) = 2x + 3x 2 y y

Question:

function of two variables is given by f(x, y) = 2x + 3x²y − y².
(a) Find expressions for the first-order and second-order partial derivatives of f.
(b) Evaluate f_x(1, 2) and f_y(1, 2), and use the small increments formula to estimate the change in f as x increases by 0.2 and y decreases by 0.1 at the point (1, 2).
(c) A curve is defined implicitly by 2x + 3x²y − y² = 4. Verify that (1, 2) lies on this curve and find the gradient at this point.