Compute and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$
-$$f ( x ) = 9 x - 11$$
A) $\frac { 11 } { 9 }$
B) -11h
C) 9
D) 11

Question

Quizplus · Accepted Answer

The difference quotient for the function $f(x) = 9x - 11$ is computed as follows: $$\frac{f(x+h) - f(x)}{h} = \frac{(9(x+h) - 11) - (9x - 11)}{h} = \frac{9x + 9h - 11 - 9x + 11}{h} = \frac{9h}{h} = 9.$$ This simplifies to 9, indicating that the rate of change of the function is constant and equal to 9.

Compute 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

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