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Ex 6.2, 2 - Show that f(x) = e2x is strictly increasing on R

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Ex 6.2, 2 Show that the function given by f (x) = e2x is strictly increasing on R. Let 𝑥1 and 𝑥2 be real numbers Such that 𝒙𝟏 < 𝒙2 Multiplying both sides by 2 2𝑥1 < 2𝑥2 Taking exponential both sides 𝑒^2𝑥1 < 𝑒^2𝑥2 f (𝒙𝟏) < f ( 𝒙2) Hence, when x1 < x2 , f(x1) < f(x2) Thus, f(x) is strictly increasing on R.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.