Question

The limit represents the derivative of some function f(x) at some number a. Find f(x) and a.

Limit as 'h' approaches 0, ((2+h)^3-8)/(h)

Answer 1

\[f'(x) = \lim_{h \rightarrow 0}\frac{ f(x+h)-f(x) }{ h }\]

Answer 2

\[f(x) = x^3\]

Answer 3

and a=2

Answer 4

How'd you come up with that?

Answer 5

That first equation is the definition of the derivative. if you plug in your values you can figure out that the 8 must come from 2^3 (so f(x)=x^3) and the 'a' must =2. It wasn't so much a solution as just looking at which locations the values were plugged into