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

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

Question

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

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

Quizplus · Accepted Answer

The expression $f(x + \Delta x, y) - f(x, y)$ calculates the change in the function $f$ as $x$ changes by $\Delta x$, with $y$ held constant. Substituting $x + \Delta x$ into $f$, we get $f(x + \Delta x, y) = (x + \Delta x) + 2y$. Subtracting $f(x, y) = x + 2y$ from this gives $(x + \Delta x + 2y) - (x + 2y) = \Delta x$.

Let f(x,y)=x+2yf ( x , y ) = x + 2 yf(x,y)=x+2y

Let $f ( x , y ) = x + 2 y$