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Ex 6.5,4 - Chapter 6 Class 12 Application of Derivatives - Part 3

Ex 6.5,4 - Chapter 6 Class 12 Application of Derivatives - Part 4

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Ex 6.5, 4 Prove that the following functions do not have maxima or minima: (iii) β„Ž(π‘₯)= π‘₯^3+π‘₯^2+π‘₯+1Given h (x) = x3 + x2 + x + 1 Finding maxima or minima β„Žβ€™ (π‘₯) = 3π‘₯^2+2π‘₯+1 Putting β„Žβ€™ (π‘₯)= 0 3π‘₯^2+2π‘₯+1=0 For ax2 + bx + c = 0 x = (βˆ’π‘ Β± √(𝑏^2 βˆ’ 4π‘Žπ‘))/2π‘Ž Here π‘Ž = 3, b = 2, & c = 1 x = (βˆ’ 2 Β± √(4 βˆ’ 4(3)(1)))/6 x = (βˆ’ 2 Β± √(4 βˆ’ 12))/6 x = (βˆ’2 Β± √(βˆ’ 8))/6 x = (βˆ’ 2 Β± 2√(βˆ’ 2))/6 x = (βˆ’πŸ Β± √(βˆ’ 𝟐))/πŸ‘ Since root has minus sign, x has no real value ∴ h (x) does not have a maxima of minima

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