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Example 26 - Find maximum and minimum values of f(x) = x2 - Finding minimum and maximum values from graph

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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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Example 26 Find the maximum and the minimum values, if any, of the function f given by f (𝑥) = 𝑥2 , 𝑥 ∈ R f﷐𝑥﷯=﷐𝑥﷮2﷯ First we plot the graph of ﷐𝑥﷮2﷯ Note that at 𝑥 = 0 f﷐0﷯=0 Also we note that f﷐𝑥﷯>0 for all 𝑥 , 𝑥 ∈ R except 0 So minimum value of f﷐𝒙﷯=𝟎 at 𝒙 = 0 Since f﷐𝑥﷯>0 for 𝑥 ∈ R expect 0 So, we can not find a maximum value e.g. f﷐100﷯=﷐﷐100﷯﷮2﷯= 10000 f﷐1000﷯= ﷐﷐1000﷯﷮2﷯= 1000000 Hence , we cannot find a maximum value of f﷐𝒙﷯ on , 𝒙 ∈ R

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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