# Ex 6.2,14 - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at April 14, 2021 by Teachoo

Last updated at April 14, 2021 by Teachoo

Transcript

Ex 6.2, 14 Find the least value of a such that the function f given by π (π₯) = π₯2 + ππ₯ + 1 is strictly increasing on (1, 2).We have f(π₯) = π₯2 + aπ₯ + 1 And, fβ(π₯) = 2π₯ + a Given f is strictly increasing on (1 ,2) β΄ fβ(π₯) > 0 on (1 ,2) Putting value of fβ(x) 2π₯ + a > 0 on (1 ,2) Letβs put x = 1 and x = 2 and find value of a So, a > β2 satisfies both equations Thus, we can say that When a > β2 , f(π₯) = π₯2 + aπ₯ + 1 is strictly increasing on (1 , 2) Hence, least value of a is β2 Putting π = 1 2(1) + a > 0 2 + a > 0 a > β2 Putting π = 2 2(2) + a > 0 4 + a > 0 a > β4

Chapter 6 Class 12 Application of Derivatives (Term 1)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.