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
  2. Serial order wise

Transcript

Example 10 Find the intervals in which the function f given by f (x) = x2 โ€“ 4x + 6 is (a) strictly increasing (b) strictly decreasingf (๐‘ฅ) = ๐‘ฅ2 โ€“ 4๐‘ฅ + 6 Calculate fโ€™(๐’™) ๐‘“โ€™ (๐‘ฅ) = 2๐‘ฅ โ€“ 4 Calculate fโ€™(๐’™) = 0 2๐‘ฅ โ€“ 4 = 0 2๐‘ฅ = 4 ๐‘ฅ = 4/2=2 Hence ๐‘ฅ = 2 divide real line into 2 disjoint intervals. Plotting points on number line Hence. f is strictly decreasing in interval (โˆ’ โˆž ,๐Ÿ) f is strictly increasing in interval (2 , โˆž)

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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.