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

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Ex 6.5,3 - Chapter 6 Class 12 Application of Derivatives - Part 7

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Ex 6.5,3 - Chapter 6 Class 12 Application of Derivatives - Part 8 Ex 6.5,3 - Chapter 6 Class 12 Application of Derivatives - Part 9

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

Transcript

Ex 6.5, 3 Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (iii) β„Ž(π‘₯)=sin⁑π‘₯+cos⁑π‘₯, 0<π‘₯<πœ‹/2 β„Ž(π‘₯)=sin⁑π‘₯+cos⁑π‘₯, 0<π‘₯<πœ‹/2 Finding 𝒉′(𝒙) β„Žβ€²(π‘₯)=𝑑(sin⁑π‘₯ + cos⁑π‘₯" " )/𝑑π‘₯ β„Ž^β€² (π‘₯)=cos⁑π‘₯βˆ’sin⁑π‘₯ Putting 𝒉′(𝒙)=𝟎 cos⁑π‘₯βˆ’π‘ π‘–π‘›π‘₯=0 cos⁑〖π‘₯=𝑠𝑖𝑛 π‘₯γ€— 1 = sin⁑π‘₯/cos⁑π‘₯ 1 = tan π‘₯ tan π‘₯=1 ∴ π‘₯=45Β°= πœ‹/4 Finding h’’(𝒙) h’(π‘₯)=cos⁑π‘₯βˆ’sin⁑π‘₯ h’’(π‘₯)=βˆ’sin⁑π‘₯βˆ’cos⁑π‘₯ Putting 𝒙=𝝅/πŸ’ h’’(Ο€/4)=βˆ’sin(Ο€/4)βˆ’π‘π‘œπ‘ (Ο€/4) = – 1/√2βˆ’1/√2 = (βˆ’2)/√2 = – √2 Since h’’(π‘₯)<0 when π‘₯=Ο€/4 ∴ π‘₯=Ο€/4 is point of Local Maxima f has Maximum value at 𝒙=𝝅/πŸ’ f(π‘₯)=𝑠𝑖𝑛π‘₯+π‘π‘œπ‘ π‘₯ f(Ο€/4)=𝑠𝑖𝑛(Ο€/4)+π‘π‘œπ‘ (Ο€/4) = 1/√2+1/√2 = 2/√2 = √𝟐

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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.