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

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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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Ex 6.5,9 What is the maximum value of the function sin⁡𝑥+cos⁡𝑥? Let f﷐𝑥﷯=﷐sin﷮𝑥﷯+﷐cos﷮𝑥﷯ Consider the interval 𝑥 ∈ ﷐0 , 2𝜋﷯ Step 1: Finding f’﷐𝑥﷯ f’﷐𝑥﷯=﷐𝑑﷐﷐sin﷮𝑥﷯ + ﷐cos﷮𝑥﷯﷯﷮𝑑𝑥﷯ f’﷐𝑥﷯=﷐cos﷮𝑥﷯−﷐sin﷮𝑥﷯ Step 2: Putting f’﷐𝑥﷯=0 ﷐cos﷮𝑥﷯−﷐sin﷮𝑥﷯=0 ﷐cos﷮𝑥﷯=﷐sin﷮𝑥﷯ 1 =﷐﷐sin﷮𝑥﷯﷮﷐cos﷮𝑥﷯﷯ 1= tan⁡𝑥 tan 𝑥=1 Since 𝑥 ∈ ﷐0 , 2𝜋﷯ tan 𝑥=1 at 𝑥=﷐𝜋﷮4﷯ , 𝑥=﷐5𝜋﷮4﷯ in the interval ﷐0 , 2𝜋﷯ Step 3: We have given the interval 𝑥 ∈ ﷐0 , 2𝜋﷯ Hence Calculating f﷐𝑥﷯ at 𝑥=0 ,﷐𝜋﷮4﷯ , ﷐5𝜋﷮4﷯ & 2𝜋 Hence Maximum Value of f﷐𝑥﷯ is ﷐﷮𝟐﷯ at 𝒙 = ﷐𝝅﷮𝟒﷯

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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