Example 10 - Find the intervals in which f(x) = x2 - 4x + 6

Example 10 - Chapter 6 Class 12 Application of Derivatives - Part 2

  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Example 10 Find the intervals in which the function f given by f (x) = x2 – 4x + 6 is (a) strictly increasing (b) strictly decreasingf (π‘₯) = π‘₯2 – 4π‘₯ + 6 Calculate f’(𝒙) 𝑓’ (π‘₯) = 2π‘₯ – 4 Calculate f’(𝒙) = 0 2π‘₯ – 4 = 0 2π‘₯ = 4 π‘₯ = 4/2=2 Hence π‘₯ = 2 divide real line into 2 disjoint intervals. Plotting points on number line Hence. f is strictly decreasing in interval (βˆ’ ∞ ,𝟐) f is strictly increasing in interval (2 , ∞)

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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.