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MHT CET2019Evening ShiftMathematicsApplication of DerivativesActual

Using differentiation, approximate value of f x = x 2 - 2 x + 1 at x = 2.99 is ….

Options

  1. A3.96
  2. B9.96
  3. C4.98
  4. D5.98

Correct answer

A. 3.96

Step-by-step solution

Given function, f x = x 2 - 2 x + 1 ⇒ f ' x = 2 x - 2 Let x = 3 and Δ x = - 0.01 So that f x + Δ x = f 2.99 We know that, f x + Δ x ≈ f x + Δ x f ' x ≈ x 2 - 2 x + 1 + - 0.01 2 x - 2 Putting x = 3 and Δ x = - 0.01 , we get f 2.99 ≈ 3 2 - 2 × 3 + 1 + - 0.01 2 × 3 - 2 ≈ 4 + - 0.01 4 ≈ 4 - 0.04 ≈ 3.96

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