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AP EAMCET2009MathematicsApplication of Derivatives

The function f(x)=x^3+a x^2+b x+c, a^2 3 b has

Options

  1. Aone maximum value
  2. Bno extreme value
  3. Cone maximum and one minimum value
  4. Done maximum and one minimum value

Correct answer

C. one maximum and one minimum value

Step-by-step solution

Given, f(x)=x^3+a x^2+b x+c, a^2 3 b . On differentiating w.r.t. x , we get aligned & f^ (x)=3 x^2+2 a x+b & Put f^ (x)=0 & 3 x^2+2 a x+b=0 & aligned aligned x & = -2 a 4 a^2-12 b 2 3 & = -2 a 2 a^2-3 b 3 aligned Since, a^2 3 b , x has an imaginary value. Hence, no extreme value of x exist.

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