Given: f(x)=x^2-1
Find a simplified form of the difference quotient.
I will be happy to critique your thinking. I am not going to do it for you. The link I gave you shows you how.
Is it set up like this
1(x+h)^2 - 1(x)
To find the difference quotient for the function f(x) = x^2-1, we need to evaluate the limit of the expression as h approaches 0.
The difference quotient is calculated by subtracting the value of the function at (x+h) from the value of the function at x, and then dividing the result by h.
Here's how you can set it up:
1. Start with the expression f(x+h) - f(x).
- For the given function f(x) = x^2-1, substitute (x+h) and x into the function to get:
f(x+h) = (x+h)^2-1
f(x) = x^2-1
2. Substitute these expressions into the difference quotient:
f(x+h) - f(x) = (x+h)^2-1 - (x^2-1)
3. Simplify the expression by expanding and combining like terms:
(x+h)^2 = x^2 + 2xh + h^2
(x+h)^2-1 = x^2 + 2xh + h^2 - 1
(x^2-1) remain the same.
Therefore, the simplified form of the difference quotient is:
[(x+h)^2-1 - (x^2-1)] / h
Remember, this is the setup for the difference quotient. To find its value, you need to evaluate the limit as h approaches 0.