Find and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$ for the given function.
-$$f ( x ) = 2 x + 9$$
A) 2
B) $2 + \frac { 18 } { h }$
C) $2 + \frac { 4 ( x + 9 ) } { h }$
D) 0

Question

Quizplus · Accepted Answer

The difference quotient for $f(x) = 2x + 9$ is calculated as follows: $$\frac{f(x+h) - f(x)}{h} = \frac{2(x+h) + 9 - (2x + 9)}{h} = \frac{2x + 2h + 9 - 2x - 9}{h} = \frac{2h}{h} = 2.$$ This simplifies to 2, indicating that the rate of change of the function is constant.

Find and Simplify the Difference Quotient f(x+h)−f(x)h,h≠0\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0hf(x+h)−f(x)​,h=0

Find and Simplify the Difference Quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$