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Ex 6.2,14 - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Chapter 6 Class 12 Application of Derivatives
Concept wise
- Finding rate of change
- To show increasing/decreasing in whole domain
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To show increasing/decreasing in intervals
- Find intervals of increasing/decreasing
- Finding slope of tangent/normal
- Finding point when tangent is parallel/ perpendicular
- Finding equation of tangent/normal when point and curve is given
- Finding equation of tangent/normal when slope and curve are given
- Finding approximate value of numbers
- Finding approximate value of function
- Finding approximate value- Statement questions
- Finding minimum and maximum values from graph
- Local maxima and minima
- Minima/ maxima (statement questions) - Number questions
- Minima/ maxima (statement questions) - Geometry questions
- Absolute minima/maxima
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
