To show increasing/decreasing in whole domain
To show increasing/decreasing in whole domain
Last updated at May 6, 2021 by Teachoo
Example 7 (Method 1) Show that the function given by f (π₯) = 7π₯ β 3 is strictly increasing on R.f(π₯) = 7π₯ β 3 Finding fβ(π) fβ(x) = (7x β 3)β fβ(x) = 7 Since fβ(π) > 0 Hence, f is strictly increasing on R Example 7 (Method 2 ) Show that the function given by f (x) = 7x β 3 is strictly increasing on R. Let π₯1 and π₯2 be real numbers Such that ππ < π2 Multiplying both sides by 7 7π₯1 < 7π₯2 Subtracting both sides by 3 7π₯1 β 3 < 7π₯2 β 3 f (ππ) < f ( π2) Hence, when x1 < x2 , f(x1) < f(x2) Thus, f(x) is strictly increasing on R.