Ex 6.5, 2 Find the maximum and minimum values, if any, of the following functions given by (iv) 𝑓 (𝑥)=|sin⁡4𝑥+3|𝑓 (𝑥)=| sin⁡4𝑥+3| We know that –1 ≤ sin θ ≤ 1 So, –1 ≤ sin 4𝑥 ≤ 1 Adding 3 both sides –1 + 3 ≤ sin 4𝑥 + 3 ≤ 1 + 3 2 ≤ sin 4𝑥 +3 ≤ 4 Taking modulus |2| ≤ | sin⁡4𝑥+3| ≤ |4| 2 ≤ | sin⁡4𝑥+3| ≤ |4| 2 ≤ f(𝑥)≤4 Hence Maximum value of f(𝒙) is 4 & Minimum value of f(𝒙) is 2

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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.

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