Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Example 7 - Chapter 6 Class 12 Application of Derivatives
Last updated at May 29, 2023 by Teachoo
To show increasing/decreasing in whole domain
Chapter 6 Class 12 Application of Derivatives
Concept wise
- Finding rate of change
-
To show increasing/decreasing in whole domain
- To show increasing/decreasing in intervals
- Find intervals of increasing/decreasing
- Finding slope of tangent/normal
- Finding point when tangent is parallel/ perpendicular
- Finding equation of tangent/normal when point and curve is given
- Finding equation of tangent/normal when slope and curve are given
- Finding approximate value of numbers
- Finding approximate value of function
- Finding approximate value- Statement questions
- Finding minimum and maximum values from graph
- Local maxima and minima
- Minima/ maxima (statement questions) - Number questions
- Minima/ maxima (statement questions) - Geometry questions
- Absolute minima/maxima
Transcript
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.
