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MHT CET202611 April 2026Morning ShiftMathematicsApplication of DerivativesActual

The approximate value of [3] 63 is

Options

  1. A3.9791
  2. B3.8791
  3. C3.9581
  4. D4.0205

Correct answer

A. 3.9791

Step-by-step solution

Let f(x) = x^ 1/3 . Let x = 64 and x = -1 . We know that f(x + x) f(x) + f'(x) x . Differentiating f(x) with respect to x , we get: f'(x) = 1 3 x^ -2/3 At x = 64 , f'(64) = 1 3 (64)^ -2/3 = 1 3 1 16 = 1 48 Now, y f'(64) x = 1 48 (-1) -0.02083 Therefore, the approximate value is: f(63) 4 - 0.02083 = 3.97917 A more precise calculation using the binomial expansion yields 3.979057 , which rounds to 3.9791 . The closest given option is 3.9791 . Answer: 3.9791

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