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Example 11 - 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
Example 11 Find the intervals in which the function f given by f (š„)=4š„3ā6š„2 ā72š„+30 is (a) strictly increasing (b) strictly decreasing. f (š„)=4š„3ā6š„2 ā72š„+30 Calculating fā(x) f (š„)=4š„3ā6š„2ā72š„+30 šā²(š„)=12š„2ā12š„ ā72š„ šā²(š„) =12(š„2āš„ ā 6) šā²(š„) =12(š„2ā3š„+2š„ ā6) šā²(š„) = 12(š„(š„ ā 3) + 2(š„ ā 3)) šā²(š)=šš(š+š)(š āš) Putting fā(x) = 0 12(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)
