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Find the difference quotient of f. Desperately Seeking HELP!!! Thank You!?
f(x+h)-f(x)/h
h is not equal to 0
f(x)=x^2-9x+2
f(x+h)-f(x)/h
1 Answer
- ?Lv 78 years ago
f(x)=x^2-9x+2, h≠0
I am not sure if it is f(x+h)-f(x)/h or [f(x+h)-f(x)]/h. So I give you both answers.
f(x+h)-f(x)/h
= [(x+h)^2 - 9(x+h) + 2] - [x^2 - 9x + 2]/h
= [(x^2 + 2hx + h^2) - (9x + 9h) + 2] - [x^2/h - 9x/h + 2/h]
= (1 - 1/h)x^2 + [2h - 9 + (9/h)]x + (h^2 - 9h + 2 - 2/h)
or
[f(x+h)-f(x)]/h
= {[(x+h)^2 - 9(x+h) + 2] - [x^2 - 9x + 2]}/h
= {[(x^2 + 2hx + h^2) - (9x + 9h) + 2] - [x^2 - 9x + 2]}/h
= {x^2 - x^2 + 2hx - 9x + 9x + h^2 + 2 - 2}/h
= {2hx + h^2}/h
= 2x + h