Question 5  CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based  for Term 1)  Solutions of Sample Papers and Past Year Papers  for Class 12 Boards
Last updated at May 29, 2023 by Teachoo
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)
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.
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