SOLUTION: For the function f(x)=x^2-8, construct and simplify the difference quotient f(h+h)-f(x)/h The difference quotient is=

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Question 151684: For the function f(x)=x^2-8, construct and simplify the difference
quotient f(h+h)-f(x)/h
The difference quotient is=
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
This is an essential component to finding the derivative of a rational function in calculus. If you continue in mathematics you will see right away that the "difference quotient" must be 2x+h.
In any case, here it is worked out:
FIRST, IDENTIFY the components:
f(x+h)=(x+h)^2-8
f(x)=x^2-8
Now, we can just substitute these into the expression:
(f(x+h)-f(x))/h=(%28%28x%2Bh%29%5E2-8%29-%28x%5E2-8%29%29%2Fh+)/h=%28x%5E2%2B2xh%2Bh%5E2-8-x%5E2%2B8%29%2Fh=%282xh%2Bh%5E2%29%2Fh=2x%2Bh
That is the answer. In calculus, we would take the limit as h goes to zero. If h is 0, 2x+h=2x. This gives the derivative of the function f(x)=x^2+c, c arbitrary. I hope you find that information interesting.