SOLUTION: Hi, I need to find and simplify the difference quotient for f(9 + h)- f(9), over h. Where f(x) = x^2 − x + 8. h cannot = 0.
Algebra ->
Functions
-> SOLUTION: Hi, I need to find and simplify the difference quotient for f(9 + h)- f(9), over h. Where f(x) = x^2 − x + 8. h cannot = 0.
Log On
Question 1067685: Hi, I need to find and simplify the difference quotient for f(9 + h)- f(9), over h. Where f(x) = x^2 − x + 8. h cannot = 0. Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website! We wish to find [f(x+h) - f(x)]/h, for h very small, and x = 9
Substituting the values in the function we get [(x+h)^2 - (x+h) + 8 - (x^2 - x + 8)]/h
Expand and simplify:
[(x^2 + 2xh + h^2 - x - h + 8 - x^2 + x - 8]/h
We see that all the x^2 and constant terms drop out and we are left with
[2xh + h^2 - h]/h -> h + 2x - 1
Substituting x = 9 gives h + 18 - 1. For h very small, this reduces to 17.
Ans: 17
