Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

If is the absolute maximum value of the expression 3 x^2+2 x-1 x^2+x+1 x R , then [ ] is __________ (where [.] denotes the greatest integer function)

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Step-by-step solution

aligned & Let y= 3 x^2+2 x-1 x^2+x+1 & (y-3) x^2+(y-2) x+y+1=0 & As x R, D 0 (y-2)^2-4(y-3)(y+1) 0 & 3 y^2-4 y-16 0 aligned Clearly y lies between the roots. Roots of the equation 3 y^2-4 y-16=0 are y= 4 208 6 = 2 52 3 Absolute maximum of the expression = 2+ 52 3 = [ ]=3

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