Answer:
The difference quotient of f is 8. Option C
Explanation:
Difference Quotient
Given a function f(x), the difference quotient is defined as
[tex]\displaystyle d=\frac{f(h+h)-f(x)}{h},\ h\neq 0[/tex]
The function provided in the question is
[tex]f(x)=8x+1[/tex]
Find f(x+h) by substituting x by x+h:
[tex]f(x+h)=8(x+h)+1[/tex]
[tex]f(x+h)=8x+8h+1[/tex]
Now compute:
[tex]\displaystyle d=\frac{8x+8h+1-(8x+1)}{h}[/tex]
Operating:
[tex]\displaystyle d=\frac{8x+8h+1-8x-1}{h}[/tex]
Simplifying:
[tex]\displaystyle d=\frac{8h}{h}[/tex]
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.
