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AP EAMCET2014MathematicsApplication of Derivatives

The condition that f(x)=a x^3+b x^2+c x+d has no extreme value, is

Options

  1. Ab^2>3 a c
  2. Bb^2=4 a c
  3. Cb^2=3 a c
  4. Db^2 < 3 a c

Correct answer

D. b^2 < 3 a c

Step-by-step solution

Given curve is f(x)=a x^3+b x^2+c x+d On differentiating w.r.t. x , we get f^ (x)=3 a x^2+2 b x+c For extremum, f^ (x)=0 3 a x^2+2 b x+c=0 Since, it has no extremum value array cl & b^2-4 a c < 0 & (2 b)^2-4 3 a c < 0 & 4 b^2-12 a c < 0 & b^2-3 a c < 0 & b^2 < 3 a c array

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