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JEE Main20249 Apr 2024Morning ShiftMathematicsApplication of DerivativesActual

Let the set of all positive values of , for which the point of local minimum of the function (1+x ( ^2-x^2 ) ) satisfies x^2+x+2 x^2+5 x+6 < 0 , be ( , ) . Then ^2+ ^2 is equal to _________

Correct answer

0

Step-by-step solution

aligned & x^2+x+2 x^2+5 x+6 aligned & x (-3,-2) . .(1) & f(x)=1+x ( ^2-x^2 ) aligned Finding local minima f^ (x)= ( ^2-x^2 )+(-2 x) x Put f ^ ( x )=0 aligned & ^2=3 x^2 & x= 3 aligned We want local min x = - 3 from (1) x (-3,-2) aligned & -3 >2 3 & =2 3 , =3 3 & ^2+ ^2=12+27=39 aligned

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