Derivatives

[kcbows]

How do I find what function is being differentiated?

 

[Otis]

Hi kc. Have you learned the Difference Quotient?

Given a function f(x), the Difference Quotient is:

[ f(x+h) - f(x) ] / h

You need to find a function whose Difference Quotient matches the rational expression in the given limit (at x = 0).

Hint: Consider horizontally-shifted parabolas.

?

 

[Steven G]

Note that (h-3)^2 - 9 = (-3+h)^2 - 9 = (-3+h)^2 - (-3)^2
Now does this math the numerator for the difference quotient that Otis quoted in the last post? What is f(x)? What does x equal?