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AP EAMCET201823 Apr 2018Evening ShiftMathematicsApplication of DerivativesActual

The constant c of Lagrange's mean value theorem for f(x)= x- 2 x in [- 2 , 2 ] is

Options

  1. A0
  2. B⁻¹ ( 1 33 8 )
  3. C⁻¹ ( 1 33 8 )
  4. D4

Correct answer

B. ⁻¹ ( 1 33 8 )

Step-by-step solution

The given function f(x)= x- 2 x , is a continuous function in interval [- 2 , 2 ] and differentiable in interval (- 2 , 2 ) . Now, according to Lagrange's mean value theorem, there exist c (- 2 , 2 ) , such that aligned & f^ (c)= f ( 2 )-f (- 2 ) 2 - (- 2 ) & - c-2 (2 c)=0 c+2-4 ^2 c=0 & 4 ^2 c- c-2=0 & So, c= 1 1+32 8 & c= 1 33 8 c= ⁻¹ ( 1 33 8 ) aligned

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