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Ex 6.5, 8 - At what points in interval [0, 2pi], does sin 2x

Ex 6.5,8 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.5,8 - Chapter 6 Class 12 Application of Derivatives - Part 3 Ex 6.5,8 - Chapter 6 Class 12 Application of Derivatives - Part 4 Ex 6.5,8 - Chapter 6 Class 12 Application of Derivatives - Part 5

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Ex 6.5, 8 At what points in the interval [0, 2Ο€ ], does the function sin 2π‘₯ attain its maximum value? Let f(π‘₯)=sin⁑2π‘₯, π‘₯ ∈ [0 , 2πœ‹] Finding f’(𝒙) f’(π‘₯)=𝑑(sin⁑2π‘₯ )/𝑑π‘₯ f’(π‘₯)=2 cos⁑2π‘₯ Putting f’(𝒙)=𝟎 2cos 2π‘₯=0 cos 2π‘₯=0 cos 2π‘₯=cosβ‘γ€–πœ‹/2γ€— If cos π‘₯=cos⁑𝑦 Then general solution of π‘₯=2π‘›πœ‹Β±π‘¦ 2π‘₯=2π‘›πœ‹+πœ‹/2 π‘₯=(2𝑛+1) πœ‹/4 Putting n = 0 π‘₯=(0+1) πœ‹/4= πœ‹/4 Putting n = 1 π‘₯=(2+1) πœ‹/4= 3πœ‹/4 Putting n = 2 π‘₯=(2(2)+1) πœ‹/4= 5πœ‹/4 Putting n = 3 π‘₯=(2(3)+1) πœ‹/4= 7πœ‹/4 Putting n = 4 π‘₯=(2(4)+1) πœ‹/4= 9πœ‹/4 Putting n = 5 π‘₯=(2(5)+1) πœ‹/4 =11πœ‹/4>2πœ‹ Since π‘₯ ∈ [0 , 2πœ‹] So, Critical Point are π‘₯ = 0 , πœ‹/4 , 3πœ‹/4 , 5πœ‹/4 , 7πœ‹/4 & 2Ο€ Finding value of f(x) at critical points i.e. π‘₯ = 0 , πœ‹/4 , 3πœ‹/4 , 5πœ‹/4 , 7πœ‹/4 & 2Ο€

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.