If $f ( x ) = - 2 x ^ { 2 } + x$, find the following limit, if it exists.
$$\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$$
A) $- 4 x + 1$
B) $- 2 x + 1$
C) $2 x + 1$
D) $- 4 x$
E) The limit does not exist.

Question

Quizplus · Accepted Answer

To find the limit, we first calculate $f(x+h)$ and then subtract $f(x)$ from it, all over $h$. This gives us the derivative of $f(x)$ at $x$, which is $-4x + 1$.

If f(x)=−2x2+xf ( x ) = - 2 x ^ { 2 } + xf(x)=−2x2+x

If $f ( x ) = - 2 x ^ { 2 } + x$