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MHT CET202521 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

The abscissae of the points of the curve y =x^3 are in the interval [-2,2] , where the slope of the tangents can be obtained by mean value theorem for the interval [-2,2] are

Options

  1. A0
  2. B3
  3. C2 3
  4. D3 2

Correct answer

C. 2 3

Step-by-step solution

Applying the Mean Value Theorem to the function f(x) = x^3 on the interval [-2, 2] : f(x) is a polynomial, hence continuous and differentiable throughout, satisfying the MVT conditions. The derivative f'(x) = 3x^2 , and the average rate of change is: f(2) - f(-2) 2 - (-2) = 8 - (-8) 4 = 4 Setting f'(c) = 4 yields: 3c^2 = 4 c^2 = 4 3 c = 2 3 Both values lie in (-2, 2) , giving the abscissae where the tangent slope equals the secant slope. The final answer is C

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