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Ex 6.3,9 - Chapter 6 Class 12 Application of Derivatives
Last updated at June 12, 2023 by Teachoo
Ex 6.3
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Ex 6.3, 27 (MCQ)
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Transcript
Ex 6.3, 9 What is the maximum value of the function sin𝑥+cos𝑥? Let f(𝑥)=sin𝑥+cos𝑥 Consider the interval 𝑥 ∈ [0 , 2𝜋] Finding f’(𝒙) f’(𝑥)=𝑑(sin𝑥 + cos𝑥 )/𝑑𝑥 f’(𝑥)=cos𝑥−sin𝑥 Putting f’(𝒙)=𝟎 cos𝑥−sin𝑥=0 cos𝑥=sin𝑥 1 =sin𝑥/cos𝑥 1= tan𝑥 tan 𝑥=1 Since 𝑥 ∈ [0 , 2𝜋] tan 𝑥=1 at 𝑥=𝜋/4 , 𝑥=5𝜋/4 in the interval [0 , 2𝜋] 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
