JEE Main 2008Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002Suppose the cubic x3−px+q{x^3} - px + qx3−px+q has three distinct real roots where p>0p>0p>0 and q>0q>0q>0. Then which one of the following holds?AOption A. The cubic has minima at p3\sqrt {{p \over 3}}3p and maxima at −p3-\sqrt {{p \over 3}}−3pBOption B. The cubic has minima at −p3-\sqrt {{p \over 3}}−3p and maxima at p3\sqrt {{p \over 3}}3pCOption C. The cubic has minima at both p3\sqrt {{p \over 3}}3p and −p3-\sqrt {{p \over 3}}−3pDOption D. The cubic has maxima at both p3\sqrt {{p \over 3}}3p and −p3-\sqrt {{p \over 3}}−3pCheckSkip · show solution
