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Example 7 - Chapter 6 Class 12 Application of Derivatives
Last updated at August 25, 2026 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 (๐ฅ) = 7๐ฅ โ 3 is strictly increasing on R.f(๐ฅ) = 7๐ฅ โ 3 Finding fโ(๐) fโ(x) = (7x โ 3)โ fโ(x) = 7 Since fโ(๐) > 0 Hence, f is strictly increasing on R Example 7 (Method 2 ) Show that the function given by f (x) = 7x โ 3 is strictly increasing on R. Let ๐ฅ1 and ๐ฅ2 be real numbers Such that ๐๐ < ๐2 Multiplying both sides by 7 7๐ฅ1 < 7๐ฅ2 Subtracting both sides by 3 7๐ฅ1 โ 3 < 7๐ฅ2 โ 3 f (๐๐) < f ( ๐2) Hence, when x1 < x2 , f(x1) < f(x2) Thus, f(x) is strictly increasing on R.
