Find the intervals in which the function f given by f (x) = x2 – 4x + 6 is strictly increasing:
(a) (-∞, 2) ∪ (2,∞)   (b) (2,∞)
(c) (-∞, 2)                (d) (-∞, 2] ∪ (2,∞)  

This question is inspired from - Example 10 - Chapter 6 Class 12 Application of Derivatives

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Question 5 Find the intervals in which the function f given by f (x) = x2 – 4x + 6 is strictly increasing: (a) (−∞, 2) ∪ (2,∞) (b) (2,∞) (c) (−∞, 2) (d) (−∞, 2] ∪ (2,∞) f(𝑥) = 𝑥2 – 4𝑥 + 6 Calculate f’(𝒙) 𝑓’ (𝑥) = 2𝑥 – 4 Calculate f’(𝒙) = 0 2𝑥 – 4 = 0 2𝑥 = 4 𝑥 = 4/2=2 Hence 𝑥 = 2 divide real line into 2 disjoint intervals. Plotting points on number line Hence. f is strictly increasing in interval (2 , ∞) So, the correct answer is (b)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.