find the difference quotient $\\frac{f(x + h)-f(x)}{h}$ for the function and simplify it.\n$f(x)=8x$\nthe…

find the difference quotient $\\frac{f(x + h)-f(x)}{h}$ for the function and simplify it.\n$f(x)=8x$\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$f(x)=8x$\nthe difference quotient is $\\square$.\n(simplify your answer. do not factor.)

Answer

Explanation:

Step1: Find ( f(x + h) )

Given ( f(x)=8x ), then ( f(x + h)=8(x + h)=8x+8h )

Step2: Substitute into the difference quotient formula

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{(8x + 8h)-8x}{h}\ \end{align*} ]

Step3: Simplify the numerator

((8x + 8h)-8x=8h), so (\frac{(8x + 8h)-8x}{h}=\frac{8h}{h})

Step4: Cancel out ( h )

Since ( h\neq0 ), (\frac{8h}{h}=8)

Answer:

(8)