An important calculation in calculus is the evaluation of the expression $$\frac { f ( x + h ) - f ( x ) } { h } , \text { where } h \neq 0 \text {. Find } \frac { f ( x + h ) - f ( x ) } { h }$$
-$$f ( x ) = 9 x + 6$$
A) 6
B) 9
C) $- 6 + 2 h$
D) $- 9$

Question

Quizplus · Accepted Answer

This expression represents the difference quotient, which is used to find the slope of the secant line between two points on a graph of $f(x)$. For $f(x) = 9x + 6$, substitute $f(x + h)$ and $f(x)$ into the expression: $\frac{(9(x + h) + 6) - (9x + 6)}{h}$. Simplify to get $\frac{9x + 9h + 6 - 9x - 6}{h} = \frac{9h}{h} = 9$.

An Important Calculation in Calculus Is the Evaluation of the Expression