Let $f ( x , y ) = x y + 3$ . Then $f ( x , y + \Delta y ) - f ( x , y )$ is

A) $\Delta x \Delta y$
B) $x - 3 \Delta y$
C) $x + 3 \Delta y$
D) $x \Delta y$
E) $x ( \Delta y ) ^ { 2 }$

Question

Let $f ( x , y ) = x y + 3$ . Then $f ( x , y + \Delta y ) - f ( x , y )$ is

A) $\Delta x \Delta y$
B) $x - 3 \Delta y$
C) $x + 3 \Delta y$
D) $x \Delta y$
E) $x ( \Delta y ) ^ { 2 }$

Quizplus · Accepted Answer

To find $f(x, y + \Delta y) - f(x, y)$, we substitute $y + \Delta y$ into the function and subtract $f(x, y)$ from it. This gives us $f(x, y + \Delta y) = x(y + \Delta y) + 3 = xy + x\Delta y + 3$. Subtracting $f(x, y) = xy + 3$ from this, we get $xy + x\Delta y + 3 - (xy + 3) = x\Delta y$.

Let f(x,y)=xy+3f ( x , y ) = x y + 3f(x,y)=xy+3

Let $f ( x , y ) = x y + 3$