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AP EAMCET2007MathematicsApplication of Derivatives

The condition f(x)=x^3+p x^2+q x+r(x R) to have no extreme value, is

Options

  1. Ap^2 < 3 q
  2. B2 p^2 < q
  3. Cp^2 < 1 4 q
  4. Dp^2>3 q

Correct answer

A. p^2 < 3 q

Step-by-step solution

Given, f(x)=x^3+p x^2+q x+r Now, f^ (x)=3 x^2+2 x p+q Clearly f^ (x)>0 Now, b^2-4 a c < 0 4 p^2-4 3 q < 0 array rrr & 4 p^2-12 q < 0 & p^2 < 3 q array

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