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Ex 6.2, 5 - Chapter 6 Class 12 Application of Derivatives
Last updated at May 29, 2023 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
Transcript
Ex 6.2, 5 Find the intervals in which the function f given by f (π₯) = 2π₯3 β 3π₯2 β 36π₯ + 7 is (a) strictly increasing (b) strictly decreasingf(π₯) = 2π₯3 β 3π₯2 β 36π₯ + 7 Calculating fβ(π) fβ(π₯) = 6π₯2 β 6π₯ β 36 + 0 fβ(π₯) = 6 (π₯2 β π₯ β 6 ) fβ(π₯) = 6(π₯^2 β 3π₯ + 2π₯ β 6) fβ(π₯) = 6(π₯(π₯ β 3) + 2 (π₯ β 3)) fβ(π) = 6(π β 3) (π + 2) Putting fβ(x) = 0 6(π₯+2)(π₯ β3)=0 (π₯+2)(π₯ β3)=0 So, x = β2 and x = 3 Plotting points on number line Hence, f is strictly increasing in (ββ ,βπ) & (π ,β) f is strictly decreasing in (βπ, π)
