Ex 6.5, 4 Prove that the following functions do not have maxima or minima: (iii) ℎ(𝑥)= 𝑥^3+𝑥^2+𝑥+1Given h (x) = x3 + x2 + x + 1 Finding maxima or minima ℎ’ (𝑥) = 3𝑥^2+2𝑥+1 Putting ℎ’ (𝑥)= 0 3𝑥^2+2𝑥+1=0 For ax2 + bx + c = 0 x = (−𝑏 ± √(𝑏^2 − 4𝑎𝑐))/2𝑎 Here 𝑎 = 3, b = 2, & c = 1 x = (− 2 ± √(4 − 4(3)(1)))/6 x = (− 2 ± √(4 − 12))/6 x = (−2 ± √(− 8))/6 x = (− 2 ± 2√(− 2))/6 x = (−𝟏 ± √(− 𝟐))/𝟑 Since root has minus sign, x has no real value ∴ h (x) does not have a maxima of minima

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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