Example 14 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 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)^2 = 10000 f(1000)= (1000)^2 = 1000000 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.