Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ for $f ( x ) = 2 + 6 x$.
A) $- 6$
B) $- 4$
C) 6
D) 2
E) limit does not exist

Question

Quizplus · Accepted Answer

This limit represents the definition of the derivative of $f(x)$ at $x$. Substituting $f(x + h) = 2 + 6(x + h)$ and $f(x) = 2 + 6x$ into the expression, simplifying, and taking the limit as $h$ approaches 0 gives $6$, which means the slope of the tangent to the function $f(x) = 2 + 6x$ is constant at $6$.

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