The limit below represents a derivative 𝑓′(𝑎) . Find 𝑓(𝑥) and 𝑎 . lim ℎ→0 [(4+ℎ)4−256]/ℎ , f(x) = ? and a = ?

Answer 1

f'(x) = lim_h→0 [(f(x+h) - f(x)) / h

Let f(x) = x⁴ and x = 4

Then f'(4) = lim_h→0 [((4+h)⁴ - 256) / h] = 4(4)³ = 256