Let f (x, y) = 3x² + 2xy + 5y, as in Example 5. Show that f (1 + h, 4) - f (1, 4) = 14h + 3h². Thus, the error in approximating f (1 + h, 4) - f (1, 4) by 14h is 3h². (If h = .01, for instance, the error is only .0003.)

Example 5

Interpret the partial derivatives of f(x, y) = 3x² + 2xy + 5y calculated in Example 4.