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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.