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Example 15 - Chapter 6 Class 12 Application of Derivatives
Last updated at April 16, 2024 by Teachoo
Finding minimum and maximum values from graph
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
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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 15 Find the maximum and minimum values of f , if any, of the function given by f(x) = |x|, x ∈ R. 𝑓(𝑥)=|𝑥|={█(−&𝑥, 𝑥<0@&𝑥, 𝑥≥0)┤ At x = 0 f(0)=0 And, we note that f(𝑥)>0 for all 𝑥 except 0 Thus, Minimum value of f(𝑥)=𝟎 at 𝒙 = 0 Also, Since f(𝒙)>𝟎 for all 𝑥 except 0 So, we cannot find a maximum value Example: f(100)=|100|=100 f(1000)= |1000|=1000 Hence , we cannot find maximum value of f(𝑥) on 𝒙 ∈ R
