Using diffe

Let us assume that

Also, let x = 27 so that x + Δx = 25

⇒ 27 + Δx = 25

∴ Δx = –2

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

We know

When x = 27, 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 = (0.03704)(–2)

∴ Δf = –0.07408

Now, we have f(25) = f(27) + Δf

⇒ f(25) = 3 – 0.07408

∴ f(25) = 2.92592

Thus, (25)^1/3 ≈ 2.92592