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

This limit represents the derivative of $f(x)$ at $x$, calculated using the definition of the derivative. By substituting $f(x+h)$ and $f(x)$ into the expression and simplifying, we find the derivative of $f(x) = -2x^2 + x$ to be $-4x + 1$.

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

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