How do I find the difference quotient
f(x)=2x^2-4x
start with f(x+h)
f(x+h)=2(x+h)^2 - 4(x+h)
work that out, then
f(x)=2x^2-4x
Then subtract f(x) from f(x+h). then divide by h.
http://www.analyzemath.com/calculus/Differentiation/difference_quotient.html
I got 8x+2h is that correct?
no wait...I did that wrong. I forgot a step.
is the answer
2x+h+2
To find the difference quotient of a function, you need to evaluate the expression (f(x + h) - f(x)) / h, where h represents a small change in x.
Let's go through the steps to find the difference quotient for the given function, f(x) = 2x^2 - 4x.
Step 1: Replace f(x) with the given function expression:
f(x) = 2x^2 - 4x
Step 2: Replace x in the function expression with (x + h):
f(x + h) = 2(x + h)^2 - 4(x + h)
Step 3: Simplify the expression:
f(x + h) = 2(x^2 + 2hx + h^2) - 4x - 4h
= 2x^2 + 4hx + 2h^2 - 4x - 4h
Step 4: Subtract f(x) from f(x + h):
f(x + h) - f(x) = (2x^2 + 4hx + 2h^2 - 4x - 4h) - (2x^2 - 4x)
Simplifying further:
f(x + h) - f(x) = 2hx + 2h^2 - 4h
Step 5: Divide the result by h:
(f(x + h) - f(x)) / h = (2hx + 2h^2 - 4h) / h
Simplifying the expression by canceling out h:
(f(x + h) - f(x)) / h = 2x + 2h - 4
So, the difference quotient for f(x) = 2x^2 - 4x is 2x + 2h - 4.