Limits and functions with a's?

Question

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

lim h->0 2(3+h)^3-54/h

State the function and the number:

f(x)=

a=

Answer 1

f'(a) = lim_h→0 [(f(a+h) - f(a)) / h]

So, if f(x) = 2x³ and if a = 3, then f(3) = 54 and f(3+h) = 2(3+h)³.

f'(3) = lim_h→0 [(2(3+h)³ - 54) / h]