How do you evaluate f(x+h)-f(x) over h if f(x)=x^2-2x?

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f(x+h)-f(x) over h

For the first part of the numerator, substitute (x+h) into f(x), or in other words, evaluate:

(x+h)^2 – 2(x+h)

The second part of the numerator is – f(x), or the negation:

2x – x^2

So the numerator is now:

(x+h)^2 – 2(x+h) + 2x – x^2, all over h.

Evaluate and simplify – eventually, you should be able to factor out an h on top, and cancel that with the denominator.

After that, any remaining terms with an “h” all are canceled out (because the limit is to 0), and you’ll be left with:

2x – 2

Hope that helps!

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