Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12



  1. Chapter 6 Class 12 Application of Derivatives
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Ex 6.5, 9 What is the maximum value of the function sin⁑π‘₯+cos⁑π‘₯? Let f(π‘₯)=sin⁑π‘₯+cos⁑π‘₯ Consider the interval π‘₯ ∈ [0 , 2πœ‹] Finding f’(𝒙) f’(π‘₯)=𝑑(sin⁑π‘₯ + cos⁑π‘₯ )/𝑑π‘₯ f’(π‘₯)=cos⁑π‘₯βˆ’sin⁑π‘₯ Putting f’(𝒙)=𝟎 cos⁑π‘₯βˆ’sin⁑π‘₯=0 cos⁑π‘₯=sin⁑π‘₯ 1 =sin⁑π‘₯/cos⁑π‘₯ 1= tan⁑π‘₯ tan π‘₯=1 Since π‘₯ ∈ [0 , 2πœ‹] tan π‘₯=1 at π‘₯=πœ‹/4 , π‘₯=5πœ‹/4 in the interval [0 , 2πœ‹] We have given the interval π‘₯ ∈ [0 , 2πœ‹] Hence Calculating f(π‘₯) at π‘₯=0 ,πœ‹/4 , 5πœ‹/4 & 2πœ‹ Hence Maximum Value of f(π‘₯) is √𝟐 at 𝒙 = 𝝅/πŸ’

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.