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Ex 6.2, 5 - Chapter 6 Class 12 Application of Derivatives
Last updated at August 2, 2026 by Teachoo
Find intervals of increasing/decreasing
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
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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, 5 Find the intervals in which the function f given by f (š„) = 2š„3 ā 3š„2 ā 36š„ + 7 is (a) strictly increasing (b) strictly decreasingf(š„) = 2š„3 ā 3š„2 ā 36š„ + 7 Calculating fā(š) fā(š„) = 6š„2 ā 6š„ ā 36 + 0 fā(š„) = 6 (š„2 ā š„ ā 6 ) fā(š„) = 6(š„^2 ā 3š„ + 2š„ ā 6) fā(š„) = 6(š„(š„ ā 3) + 2 (š„ ā 3)) fā(š) = 6(š ā 3) (š + 2) Putting fā(x) = 0 6(š„+2)(š„ ā3)=0 (š„+2)(š„ ā3)=0 So, x = ā2 and x = 3 Plotting points on number line Hence, f is strictly increasing in (āā ,āš) & (š ,ā) f is strictly decreasing in (āš, š)
