Let us assume that

Also, let x = 36 so that x + Δx = 36.6

⇒ 36 + Δx = 36.6

∴ Δx = 0.6

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

We know

When x = 36, 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 = 0.6

⇒ Δf = (0.0833333)(0.6)

∴ Δf = 0.05

Now, we have f(36.6) = f(36) + Δf

⇒ f(36.6) = 6 + 0.05

∴ f(36.6) = 6.05

Thus,