Let $f ( x , y ) = x ^ { 2 } - 2 x y$ . Then $f ( x , y + \Delta y ) - f ( x , y )$ is

A) $- \Delta x \Delta y$
B) $- 2 \Delta x \Delta y$
C) $- 2 x \Delta y$
D) $x \Delta y$
E) $2 x \Delta y$

Question

Let $f ( x , y ) = x ^ { 2 } - 2 x y$ . Then $f ( x , y + \Delta y ) - f ( x , y )$ is

A) $- \Delta x \Delta y$
B) $- 2 \Delta x \Delta y$
C) $- 2 x \Delta y$
D) $x \Delta y$
E) $2 x \Delta y$

Quizplus · Accepted Answer

To find $f(x, y + \Delta y) - f(x, y)$, we substitute $y + \Delta y$ into the original function and subtract $f(x, y)$ from it. So, $f(x, y + \Delta y) = x^2 - 2x(y + \Delta y) = x^2 - 2xy - 2x\Delta y$. Subtracting $f(x, y) = x^2 - 2xy$ from this gives $-2x\Delta y$, which matches choice C.

Let f(x,y)=x2−2xyf ( x , y ) = x ^ { 2 } - 2 x yf(x,y)=x2−2xy

Let $f ( x , y ) = x ^ { 2 } - 2 x y$