A function of two variables is given by f(x, y) = 2x + 3x2 y - y2 . (a) Find expressions for the...

A function of two variables is given by f(x, y) = 2x + 3x2 y − y2 . (a) Find expressions for the first-order and second-order partial derivatives of f. (b) Evaluate fx(1, 2) and fy(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 + 3x2 y − y2 = 4. Verify that (1, 2) lies on this curve and find the gradient at this point.