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AP EAMCET202420 May 2024Morning ShiftMathematicsApplication of DerivativesActual

If the function f(x)= x^2-4 satisfies the Lagrange's mean value theorem on [2,4] , then the value of C is

Options

  1. A2 3
  2. B-2 3
  3. C6
  4. D- 6

Correct answer

C. 6

Step-by-step solution

f(x)= x^2-4 f^ (x)= x x^2-4 f^ (C)= f(4)-f(2) 4-2 for some C [2,4] C C^2-4 = 2 3 -0 2 = 3 C^2=3 (C^2-4 ) 2 C^2=12 C^2= 6

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