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Example 7 - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 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
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Transcript
Example 7 (Method 1) Show that the function given by f (đĽ) = 7đĽ â 3 is strictly increasing on R.f(đĽ) = 7đĽ â 3 Finding fâ(đ) fâ(x) = (7x â 3)â fâ(x) = 7 Since fâ(đ) > 0 Hence, f is strictly increasing on R Example 7 (Method 2 ) Show that the function given by f (x) = 7x â 3 is strictly increasing on R. Let đĽ1 and đĽ2 be real numbers Such that đđ < đ2 Multiplying both sides by 7 7đĽ1 < 7đĽ2 Subtracting both sides by 3 7đĽ1 â 3 < 7đĽ2 â 3 f (đđ) < f ( đ2) Hence, when x1 < x2 , f(x1) < f(x2) Thus, f(x) is strictly increasing on R.
