find the difference quotient \\( \\frac { f ( x + h ) - f ( x ) } { h } \\) for the function and simplify…

find the difference quotient \\( \\frac { f ( x + h ) - f ( x ) } { h } \\) for the function and simplify it. \n\n\\( f ( x ) = 14 x \\) \n\nthe difference quotient is \\( \\square \\). \n(simplify your answer. do not factor.)

find the difference quotient \\( \\frac { f ( x + h ) - f ( x ) } { h } \\) for the function and simplify it. \n\n\\( f ( x ) = 14 x \\) \n\nthe difference quotient is \\( \\square \\). \n(simplify your answer. do not factor.)

Answer

Explanation:

Step1: Find ( f(x + h) )

Given ( f(x)=14x ), then ( f(x + h)=14(x + h)=14x+14h ).

Step2: Substitute into the difference quotient formula

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{(14x + 14h)-14x}{h}\ \end{align*} ]

Step3: Simplify the numerator

((14x + 14h)-14x=14h), so the expression becomes (\frac{14h}{h}).

Step4: Cancel out ( h )

Since (h\neq0) (in the context of the difference quotient), (\frac{14h}{h}=14).

Answer:

(14)