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JEE Main2008MathematicsApplication of DerivativesActual

Suppose the cube x^3-p x+q has three distinct real roots where p>0 and q>0 . Then which one of the following holds?

Options

  1. AThe cubic has minima at p 3 and maxima at - p 3
  2. BThe cubic has minima at - p 3 and maxima at p 3
  3. CThe cubic has minima at both p 3 and - p 3
  4. DThe cubic has maxima at both p 3 and - p 3

Correct answer

A. The cubic has minima at p 3 and maxima at - p 3

Step-by-step solution

Let f(x)=x^3-p x+q Now for maxima/minima aligned & f^ (x)=0 & 3 x^2-p=0 & x^2= p 3 & x= p 3 aligned

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