Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ for $f ( x ) = - 4 + 7 x$.
A) $- 7$
B) $- 11$
C) 7
D) $- 4$
E) limit does not exist

Question

Quizplus · Accepted Answer

This limit represents the derivative of the function $f(x) = -4 + 7x$ with respect to $x$. Calculating the derivative directly gives $f'(x) = 7$, which means the limit as $h$ approaches 0 of the given expression is 7.

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