Let us assume that

Also, let x = 64 so that x + Δx = 66

⇒ 64 + Δx = 66

∴ Δx = 2

On differentiating f(x) with respect to x, we get

We know

When x = 64, we have

Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as

Here, and Δx = 2

⇒ Δf = (0.02083)(2)

∴ Δf = 0.04166

Now, we have f(66) = f(64) + Δf

⇒ f(66) = 4 + 0.04166

∴ f(66) = 4.04166

Thus, (66)^1/3 ≈ 4.04166