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MHT CET202020 Oct 2020Morning ShiftMathematicsApplication of DerivativesActual

The minimum value of f(x)=a² ² x+b² ² x if a²>b² , is

Options

  1. Aa²-b²
  2. Bb²
  3. Ca²+b²
  4. Da²

Correct answer

D. a²

Step-by-step solution

Given f(x)=a² ² x+b² ² x=a² ( 1+ 2 x 2 )+b² ( 1- 2 x 2 )= ( a²+b² 2 )+ ( a²-b² 2 ) 2 xf(x) will be maximum when 2 x=1 f ( x ) will be minimum when 2 x =-1 Hence minimum value of f(x) is aligned f(x) &= a²+b² 2 + ( a²-b² 2 )(-1) &= a²+b² 2 - a²-b² 2 =b² aligned

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