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Ex 6.5, 9 - What is the maximum value of sin x + cos x? - Ex 6.5

Ex 6.5,9 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.5,9 - Chapter 6 Class 12 Application of Derivatives - Part 3

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.