Question

Again help, i don’t understand this at all

Answer 1

Answer:

The difference quotient of f is 8. Option C

Explanation:

Difference Quotient

Given a function f(x), the difference quotient is defined as

$\displaystyle d=\frac{f(h+h)-f(x)}{h},\ h\neq 0$

The function provided in the question is

$f(x)=8x+1$

Find f(x+h) by substituting x by x+h:

$f(x+h)=8(x+h)+1$

$f(x+h)=8x+8h+1$

Now compute:

$\displaystyle d=\frac{8x+8h+1-(8x+1)}{h}$

Operating:

$\displaystyle d=\frac{8x+8h+1-8x-1}{h}$

Simplifying:

$\displaystyle d=\frac{8h}{h}$

d=8

A.  Incorrect.

This choice is different from the answer.

B. Incorrect.

This choice is different from the answer.

C. Is correct

The difference quotient is 8 as explained above.

D. Incorrect.

This choice is different from the answer.