Helping students gain understanding and self-confidence in algebra.
GreenLantern wrote:Problem: Use the definition of f'(x) in terms to show that the derivative of is
My understanding is that I'm supposed to use the notion of the change in f(x) (also known as f'(x), correct?) to show a limit. As far as I'm concerned though, f(x) is just a parabola and doesn't ever experience the "limit" aspect anywhere so defining f'(x) as a limit seems a little silly.
GreenLantern wrote:Okay, so I'm still trying to wrap my head around this one, but I think I understand enough to make another post.
What we have normally dealt with is a limit being super super simple, like
To show that Y never actually is 1, but is always getting closer to it.
Now, the problem is asking me to show how Y is always approaching 6x-1 but never actually is.
Alright... I can do that.
So I start with my original function.
Now I make a little chart to show values to compare them.
But now I am immediately confused, because while this is normally how we showed that this was where the function never crossed we can see that it clearly does. Meaning that there is a point where f(x)=f'(x) and it's between 1&10 (I didn't take the time to find the exact point). How is this a "limit" if it does in fact cross over?