AP EAMCET202319 May 2023Morning ShiftMathematicsApplication of DerivativesActual

The maximum value of ' a ' such that the second derivative of x^4+a x^3+ 3 x^2 2 +1 is positive for all real x is

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Correct answer

C. 2

Step-by-step solution

aligned & f(x)=x^4+a x^3+ 3 x^2 2 +1 & f^ (x)=12 x^2+6 a x+3 & f^ (x)>0 4 x^2+3 a x+1>0 & (2 x+ 1 2 a )^2+ (1- a^2 4 )>0 & 1- a^2 4 >0 & a^2 4 < 1 a^2 < 4 -2 < a < 2 & Maximum value of a is 2 . aligned

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