find the difference quotient $\frac{f(x + h)-f(x)}{h}$ for the function and simplify it.\n\n$f(x)=16x$\n\nthe…

find the difference quotient $\frac{f(x + h)-f(x)}{h}$ for the function and simplify it.\n\n$f(x)=16x$\n\nthe difference quotient is \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$f(x)=16x$\n\nthe difference quotient is \n(simplify your answer. do not factor.)

Answer

Explanation:

Step1: Find f(x + h)

Given (f(x)=16x), then (f(x + h)=16(x + h)=16x+16h)

Step2: Substitute into difference - quotient formula

(\frac{f(x + h)-f(x)}{h}=\frac{(16x + 16h)-16x}{h})

Step3: Simplify the numerator

((16x + 16h)-16x=16h), so (\frac{(16x + 16h)-16x}{h}=\frac{16h}{h})

Step4: Cancel out h

(\frac{16h}{h}=16)

Answer:

16