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Example 7 - Show that f(x) = 7x - 3 is strictly increasing

Example 7 - Chapter 6 Class 12 Application of Derivatives - Part 2


Transcript

Example 7 (Method 1) Show that the function given by f (π‘₯) = 7π‘₯ – 3 is strictly increasing on R.f(π‘₯) = 7π‘₯ – 3 Finding f’(𝒙) f’(x) = (7x – 3)’ f’(x) = 7 Since f’(𝒙) > 0 Hence, f is strictly increasing on R Example 7 (Method 2 ) Show that the function given by f (x) = 7x – 3 is strictly increasing on R. Let π‘₯1 and π‘₯2 be real numbers Such that π’™πŸ < 𝒙2 Multiplying both sides by 7 7π‘₯1 < 7π‘₯2 Subtracting both sides by 3 7π‘₯1 βˆ’ 3 < 7π‘₯2 βˆ’ 3 f (π’™πŸ) < f ( 𝒙2) Hence, when x1 < x2 , f(x1) < f(x2) Thus, f(x) is strictly increasing on R.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.