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MHT CET202526 Apr 2025Morning ShiftMathematicsApplication of DerivativesActual

If y = x+ x^3-x has extreme values at x=-1 and x=1 , then and are respectively

Options

  1. A0 and 1 3
  2. B0 and -1 3
  3. C-1 3 and 1 3
  4. D1 3 and 1 3

Correct answer

A. 0 and 1 3

Step-by-step solution

Finding Extreme Values via Derivatives The function y = x + x^3 - x has extreme values where its first derivative dy dx = 0 . Differentiate term by term: dy dx = x + 3 x^2 - 1 Given extreme points at x = 1 and x = -1 , evaluate dy dx at both points: At x = 1 : 1 + 3 (1)^2 - 1 = 0 + 3 = 1 At x = -1 : -1 + 3 (-1)^2 - 1 = 0 - + 3 = 1 Add the two equations to eliminate : ( + 3 ) + (- + 3 ) = 1 + 1 6 = 2 = 1 3 Substitute = 1 3 into + 3 = 1 : + 3 1 3 = 1 + 1 = 1 = 0 The solution = 0 , = 1 3 corresponds to option A. Final

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