Example 27 - Find maximum and minimum values of f(x) = |x| - Examples

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  1. Chapter 6 Class 12 Application of Derivatives
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Example 27 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﷯﷯ First we plot graph of |x| At x = 0 Also f(x) > 0 for all x, x ∈ R except 0 Therefore the function has a minimum value 0 at 𝑥 = 0 Hence, 𝑥 = 0 is point of minima of f﷐𝑥﷯ Also f﷐𝑥﷯>0 for all 𝑥 ∈ R except 0 As f﷐−1﷯= ﷐1﷯=1 f﷐−100﷯=﷐−100﷯=100 f﷐100﷯=﷐100﷯=100 So we cannot find a maximum value Hence, there is no Maximum value of f in R & No point of Maxima value of f in R

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