find the difference quotient for function

Algebra
Tutor: None Selected Time limit: 1 Day

f(x) defined as f(a+b)-f(a) over h 

find difference quotient of fiction     f(x)=x^2+8x-9 

Oct 12th, 2015

Thank you for the opportunity to help you with your question!

f(x) = f(x+h) - f(x)/h

For f(x)=x^2+8x-9,

f(x+h)= (x+h)^2+8(x+h)-9

f(x) = x^2 - 8x - 9

So,

(x+h)^2+8(x+h)-9 - (x^2 - 8x - 9)/h

Expand and combine:

(x^2 + 2hx +h^2 + 8x + 8h - 9 - x^2 - 8x - 9) / h

= h + 2x + 8 :D


Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 12th, 2015

why does the a and b disappear? 

Oct 12th, 2015

A and b do not disappear, as such. They mean the same exact thing as x and h. You could have used h and i if you wanted. They're just variables; you can rewrite the solution I provided with any other letters :)it's similar to how you can write f(x)=x+2 or f(t)=t+2. It doesn't matter which letter you use.


Oct 12th, 2015

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