This question is similar to Chapter 6 Class 12 Application of Derivatives - Ex 6.2

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https://www.teachoo.com/4359/709/Ex-6.2--19---The-interval-in-which-y--x2-e-x-is-increasing/category/Ex-6.2/

 

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Question 3 The interval in which the function 𝑓 defined by 𝑓(𝑥)=𝑒^𝑥 is strictly increasing, is (A) [1,∞) (B) (−∞,0) (C) (−∞,∞) (D) (0,∞)f(𝑥) = 𝑒^𝑥 We need to find which interval it is strictly increasing Now, f(𝑥) = 𝑒^𝑥 f’(𝒙) = 𝒆^𝒙 And, 𝒆^𝒙>𝟎 for all values of x Therefore, f’(𝒙) >𝟎 for all values of x Thus, f(𝑥) is increasing for (−∞,∞) So, the correct answer is (C)

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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.