Ex 6.2, 14 - Find least value of a such that f(x) = x2+ax+1 - To show increasing/decreasing in intervals

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  1. Chapter 6 Class 12 Application of Derivatives
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Ex 6.2,14 Find the least value of a such that the function f given by 𝑓 (𝑥) = 𝑥2 + ğ‘Žğ‘¥ + 1 is strictly increasing on (1, 2). We have f﷐𝑥﷯ = 𝑥2 + a𝑥 + 1 Given f is strictly increasing on ﷐1 ,2ï·¯ ⇒ f’﷐𝑥﷯ > 0 on ﷐1 ,2ï·¯ f’﷐𝑥﷯ = 𝑥2 + a𝑥 + 1 f’﷐𝑥﷯ = 2𝑥 + a. Thus, 2𝑥 + a > 0 on ﷐1 ,2ï·¯ ∴ When a > –2 , f﷐𝑥﷯ = 𝑥2 + a𝑥 + 1 is strictly increasing on ﷐𝟏 , 𝟐﷯ Hence, least value of a is –2

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.