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AP EAMCET202119 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

Given f ( x ) = x 3 - 4 x , if x changes from 2 to 1 . 99 , then the approximate change in the value of f ( x ) is

Options

  1. A0.08
  2. B− 0.08
  3. C0.8
  4. D− 0.8

Correct answer

B. − 0.08

Step-by-step solution

Let, y = x 3 - 4 x , Since, we have x = 2 and ∆ x = - 0 . 01 Now, d y d x = 3 x 2 - 4   ⇒ d y d x x = 2 = 3 x 2 - 4 x = 2 = 8 So, ∆ y = d y d x ∆ x = 8 × - 0 . 01 = - 0 . 08

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