Ex 6.5, 4 - Prove that the functions do not maxima or minima

Ex 6.5,4 - Chapter 6 Class 12 Application of Derivatives - Part 2
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

  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Ex 6.5, 4 Prove that the following functions do not have maxima or minima: (i) 𝑓 (π‘₯) = 𝑒^π‘₯Given 𝑓 (π‘₯) = 𝑒^π‘₯ Finding maxima or minima 𝑓′(π‘₯) = 𝑒^π‘₯ Putting fβ€˜ (x) = 0 𝑒π‘₯ = 0 This is not possible for any value of x. ∴ f (x) does not have a maxima or minima. Ex 6.5, 4 Prove that the following functions do not have maxima or minima: (ii) g(x) = log xGiven g (x) = log x Finding maxima or minima gβ€˜ (x) = 1/π‘₯ Putting g’ (x) = 0 1/π‘₯=0 π‘₯ =1/0 π‘₯ = ∞ This is not defined for x. So, g (x) does not have a maxima or minima. 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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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.