# Misc 14 - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Misc 14 Find the absolute maximum and minimum values of the function f given by f (𝑥) = cos2 𝑥 + sin𝑥, 𝑥 ∈ [0, 𝜋 ] f𝑥=cos2𝑥+sin 𝑥 , 𝑥 ∈ 0 , 𝜋 Step 1: Finding f’𝑥 f𝑥=cos2𝑥+sin 𝑥 f’𝑥= 𝑑cos2𝑥 + sin𝑥𝑑𝑥 = 2cos 𝑥. 𝑑cos 𝑥𝑑𝑥 + cos 𝑥 = 2cos 𝑥−sin 𝑥+cos𝑥 = cos 𝑥 −2sin 𝑥+1 Step 2: Putting f’𝑥 = 0 cos 𝑥 −2sin𝑥+1=0 𝑥 = 𝜋6 & 𝜋 2 are Critical points. Since our interval is 𝑥 ∈ [0, 𝜋 ] Critical points are 𝑥=0, 𝜋6 , 𝜋2 , 𝜋 Step 3: Hence Absolute maximum value = 𝟓𝟒 & Absolute minimum value = 1

Chapter 6 Class 12 Application of Derivatives

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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.