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BITSAT2011MathematicsApplication of DerivativesActual

The function ( f ( x )=2 x ^3-3 x ^2-12 x +4 ), has

Options

  1. Atwo points of local maximum
  2. Btwo points of local minimum
  3. Cone maxima and one minima
  4. Dnomaxima or minima

Correct answer

C. one maxima and one minima

Step-by-step solution

( aligned & f(x)=2 x^3-3 x^2-12 x+4 & f^ (x)=6 x^2-6 x-12=6 (x^2-x-2 ) & =6(x-2)(x+1) aligned ) For maxima and minima ( f ^ ( x )=0 ) ( 6( x -2)( x +1)=0 x =2,-1 ) Now, ( f ^ ( x )=12 x -6 ) ( aligned & At x =2 ; f ^ ( x )=24-6=18 > 0 & x =2, local min. point & At x =-1 ; f ^ ( x )=12(-1)-6=-18 < 0 & x =-1 local max. point aligned )

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