Find
$\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ for $f ( x ) = 4 - 6 x$.
A) 6
B) 10
C) $- 6$
D) 4
E) limit does not exist

Question

Find 
$\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ for $f ( x ) = 4 - 6 x$.
A) 6
B) 10
C) $- 6$
D) 4
E) limit does not exist

Quizplus · Accepted Answer

$$\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = \lim _ { h \rightarrow 0 } \frac { ( 4 - 6 ( x + h ) ) - ( 4 - 6 x ) } { h }$$ 
$$= \lim _ { h \rightarrow 0 } \frac { - 6 h } { h } = \lim _ { h \rightarrow 0 } ( -6 ) = \boxed{-6}$$

Find lim⁡h→0f(x+h)−f(x)h\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }limh→0​hf(x+h)−f(x)​

Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$