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Ex 6.3, 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€— 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€ 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo