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
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.