Ex 6.5,5 - Chapter 6 Class 12 Application of Derivatives - Part 3

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Ex 6.5,5 - Chapter 6 Class 12 Application of Derivatives - Part 4

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Ex 6.5,5 - Chapter 6 Class 12 Application of Derivatives - Part 5

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

Transcript

Ex 6.5, 5 Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: (ii) f (π‘₯) = sin⁑π‘₯ + cos⁑π‘₯ , π‘₯ ∈ [0, πœ‹ ] Finding f’(𝒙) f’(π‘₯)=𝑑(𝑠𝑖𝑛π‘₯ + π‘π‘œπ‘ π‘₯)/𝑑π‘₯ f’(π‘₯)=cos⁑〖π‘₯ βˆ’sin⁑π‘₯ γ€— Putting f’(𝒙) cos⁑〖π‘₯ βˆ’sin⁑π‘₯ γ€—= 0 cos⁑〖π‘₯=sin⁑π‘₯ γ€— 1 = sin⁑π‘₯/(cos⁑ π‘₯) 1 = tan π‘₯ tan π‘₯ = 1 We know that know tan ΞΈ = 1 at ΞΈ = πœ‹/4 ∴ π‘₯ = πœ‹/4 Since given interval π‘₯ ∈ [0 , πœ‹] Hence calculating f(π‘₯) at π‘₯=0 , πœ‹/4 ,πœ‹ Absolute Maximum value of f(π‘₯) is √𝟐 at 𝒙 = 𝝅/πŸ’ & Absolute Minimum value of f(π‘₯) is –1 at 𝒙 = Ο€

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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.