Example 10 - Chapter 6 Class 12 Application of Derivatives (Term 1)
Last updated at April 19, 2021 by Teachoo
Find intervals of increasing/decreasing
Chapter 6 Class 12 Application of Derivatives (Term 1)
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
Example 10 Find the intervals in which the function f given by f (x) = x2 β 4x + 6 is (a) strictly increasing (b) strictly decreasingf (π₯) = π₯2 β 4π₯ + 6 Calculate fβ(π) πβ (π₯) = 2π₯ β 4 Calculate fβ(π) = 0 2π₯ β 4 = 0 2π₯ = 4 π₯ = 4/2=2 Hence π₯ = 2 divide real line into 2 disjoint intervals. Plotting points on number line Hence. f is strictly decreasing in interval (β β ,π) f is strictly increasing in interval (2 , β)
