If f(x)=alog⁡|x|+bx2+x has its extremum values  at x=-1 and x=2, then

If f(x)=alog|x|+bx2+x has its extremum values  at x=-1 and x=2, then

  1. A

    a=2,b=1

  2. B

    a=2,b=12

  3. C

    a=-2,b=12

  4. D

    none of these

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    Solution:

    We have,

    f(x)=alog|x|+bx2+xf(x)=ax+2bx+1

    Since f(x) attains its extremum values at x=-1, 2

     f(1)=0 and f(2)=0 a2b+1=0 and a2+4b+1=0 a=2 and b=1/2.

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