What's the slope of y=x^3 at x=2?

Posted on 2015-10-30 07:09:00 in Math by DOPPY

I know this is long, but please bear with me: My math class is too boring; I'm trying to teach myself calculus, so I looked up some stuff online, and I'm trying to find the slope of y=x^3 at x=2. I got an answer of 8, not sure if this is correct, but here's my work:
At x=(2+(delta)x), y=(2+(delta)x)^3

Simplify this, and we get y=8+12(delta)x+6(delta)x^2+(delta)x^3. According to the website, you divide this by (delta)x, which makes sense. Then, the slope is 8+6(delta)x+(delta)x^2, so the slope is 8. However, in the example they had, the slope was (3(delta)x+3(delta)x^2+(delta)x^3)/(delt... of which they got 3+3(delta)x+(delta)x^2. That doesn't really make a lot of sense, probably because I'm thinking of it in more "standard" terms.

Can someone please help me out? It's very much appreciated! Thanks so much!

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