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Example 19 - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
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
- Finding minimum and maximum values from graph
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Local maxima and minima
- Minima/ maxima (statement questions) - Number questions
- Minima/ maxima (statement questions) - Geometry questions
- Absolute minima/maxima
Transcript
Example 19 (Method 1) Find local minimum value of the function f given by f (𝑥) = 3 + |𝑥| , 𝑥 ∈ R. f (𝑥) = 3 + |𝑥| Since Value of |𝒙|≥𝟎 So, Minimum value of |𝑥|=0 Now, Minimum value of f (𝑥) = 3 + Minimum value of |𝑥| = 3 + 0 = 3 Hence minimum value of f (𝑥) = 3 Example 19 (Method 2) Find local minimum value of the function f given by f (𝑥) = 3 + |𝑥|, 𝑥 ∈ R. f (𝑥) = 3 + |𝑥| From graph, f (𝑥) is Minimum at 𝑥 = 0 So, Minimum value of f (𝑥) = f (0) = 3
