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MHT CET20239 May 2023Morning ShiftMathematicsApplication of DerivativesActual

The value of c of Lagrange's mean value theorem for f (x)= 25-x^2 on [1,5] is

Options

  1. A15
  2. B5
  3. C10
  4. D1

Correct answer

A. 15

Step-by-step solution

aligned & f (x)= 25-x^2 & f ^ (x= c )= -2 c 2 25- c ^2 &= - c 25- c ^2 aligned Applying Lagrange's mean value theorem, we get aligned & f ^ ( c )= f (1)- f (5) 1-5 & c 25- c ^2 = 25-1 - 25-5^2 1-5 & - c 25- c ^2 = - 24 4 aligned array ll & 4 c = 24 25- c ^2 & 16 c ^2=24 (25- c ^2 ) & c ^2=15 & c = 15 array Since c=- 15 does not lie in [1,5]c= 15

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