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AP EAMCET201920 Apr 2019Evening ShiftMathematicsApplication of DerivativesActual

If f(x)=a |x|+b x^2+x has extreme values at x=-1 and x=2 , then the ordered pair (a, b)=

Options

  1. A(2 ,-1 )
  2. B(2,- 1 2 )
  3. C(-1,2)
  4. D(- 1 2 , 2 )

Correct answer

B. (2,- 1 2 )

Step-by-step solution

Given, f(x)=a |x|+b x^2+x aligned & f^ (x)=a 1 |x| x |x| +b(2 x)+1 & f^ (x)= a x |x|^2 +2 b x+1 aligned Given that x=-1 is one of extremity of f(x) . aligned f^ (-1)= & 0 & a(-1) 1 +2 b(-1)+1=0 aligned Also, given x=2 is the other extremity of f(x) . aligned f^ (2) & =0 a(2) 4 +2 b(2)+1 & =0 a 2 +4 b+1 & =0 aligned Adding on Eqs. (i) and (ii), we get array rlrl & & 6 b+3 & =0 & b & =- 1 2 array Substituting b=- 1 2 in Eq. (i), we get aligned a & =2 (a, b) & = (2,- 1 2 ) aligned Hence option (b) is correct.

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