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Example 7 - Chapter 6 Class 12 Application of Derivatives
Last updated at July 24, 2026 by Teachoo
To show increasing/decreasing in whole domain
Chapter 6 Class 12 Application of Derivatives
Concept wise
- Finding rate of change
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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 (š„) = 7š„ ā 3 is strictly increasing on R.f(š„) = 7š„ ā 3 Finding fā(š) fā(x) = (7x ā 3)ā fā(x) = 7 Since fā(š) > 0 Hence, f is strictly increasing on R Example 7 (Method 2 ) Show that the function given by f (x) = 7x ā 3 is strictly increasing on R. Let š„1 and š„2 be real numbers Such that šš < š2 Multiplying both sides by 7 7š„1 < 7š„2 Subtracting both sides by 3 7š„1 ā 3 < 7š„2 ā 3 f (šš) < f ( š2) Hence, when x1 < x2 , f(x1) < f(x2) Thus, f(x) is strictly increasing on R.
