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Ex 6.2,18 - Chapter 6 Class 12 Application of Derivatives
Last updated at August 2, 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
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Transcript
Ex 6.2, 18 Prove that the function given by f (š„) = š„3 ā 3š„2 + 3š„ ā 100 is increasing in R. We need to show f(š„) is strictly increasing on R i.e. we need to show fā(š) > 0 Finding fā(š) fā(š„)= 3x2 ā 6x + 3 ā 0 = 3(š„2ā2š„+1) = 3((š„)2+(1)2ā2(š„)(1)) = 3(š„ā1)2 Since Square of any number is always positive (š„ā1)2 > 0 3(š„ā1)2>0 fā(š) > 0 Hence, fā(š„) > 0 for all values of š„ ā“ f(š„) is strictly increasing on R
