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Ex 6.3, 2 Find the maximum and minimum values, if any, of the following functions given by (iv) 𝑓 (π‘₯)=|sin⁑4π‘₯+3|𝑓 (π‘₯)=| sin⁑4π‘₯+3| We know that –1 ≀ sin ΞΈ ≀ 1 So, –1 ≀ sin 4π‘₯ ≀ 1 Adding 3 both sides –1 + 3 ≀ sin 4π‘₯ + 3 ≀ 1 + 3 2 ≀ sin 4π‘₯ +3 ≀ 4 Taking modulus |2| ≀ | sin⁑4π‘₯+3| ≀ |4| 2 ≀ | sin⁑4π‘₯+3| ≀ |4| 2 ≀ f(π‘₯)≀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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo