In the accompanying figure a rectangle with initial length x0 and initial width y0 has been enlarged, resulting in a rectangle with length x0 +∆x and width y0 +∆y. What portion of the figure represents the increase in the area of the rectangle? What portion of the figure represents an approximation of the increase in area by the linear approximation?
The area function is f (x, y) = x y. The area of the new rectangle is
and the approximation of the increase is y0∆x + x0∆
