Question

Using differentiation, approximate value of f(x) = x² - 2x + 1 at x = 2.99 is ______.

Options

• 3.96

• 9.96

• 4.98

• 5.98

Answer 1

Using differentiation, approximate value of f(x) = x² - 2x + 1 at x = 2.99 is 3.96.

Explanation:

Given function, f(x) = x² - 2x + 1

⇒ f'(x) = 2x - 2

Let x = 3 and Δ x = -0.01

So that f(x + Δ x) = f(2.99)

We know that, f(x + Δx) ≈ f(x) + Δx f'(x)

≈ (x² - 2x + 1) + (-0.01) (2x - 2)

putting x = 3 and Δ x = - 0.01, we get

f(2.99) ≈ (3² - 2 x 3 + 1) + (- 0.01) (2 x 3 - 2)

≈ (4) + (- 0.01)(4)

≈ 4 - 0.04

≈ 3.96