Let x = 2 and Δx = 0.01. Then, we get,

f(2.01) = f(x + Δx) = 4(x +Δx)² + 5 ( x + Δx) + 2

Now, Δy = f (x + Δx) – f(x)

⇒ f (x + Δx) = f(x) + Δy

≈ f(x) + f’(x).Δx (as dx = Δx)

⇒ f(2.01) ≈ (4x² + 5x + 2) + (8x + 5) Δx

= [4(2)² + 5(2) + 2] +[8(2) + 5] (0.01)

= (16 + 10 + 2) + (16 + 5)(0.01)

= 28 + 0.21

= 28.21

Therefore, the approximate value of f (2.01) is 28.21.