Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ for $f ( x ) = 8 - x$
A) 1
B) 9
C) $- 1$
D) 8
E) limit does not exist

Name: Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ for $f ( x ) = 8 - x$ A) 1 B) 9 C) $- 1$ D) 8 E) limit does not exist
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Question

Quizplus · Accepted Answer

The expression represents the definition of the derivative of $f(x)$ at $x$. For $f(x) = 8 - x$, $f'(x) = -1$, indicating the slope of the tangent to the curve at any point $x$ is $-1$.

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