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Find the least value of a such that the function f given by f (x) = x2 + ax + 1 is strictly increasing on [1, 2]. - Mathematics

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प्रश्न

Find the least value of a such that the function f given by f (x) = x2 + ax + 1 is strictly increasing on [1, 2].

योग
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उत्तर

We have f (x) = x2 + ax + 1

= f' (x) = 2x + a

If 1 < x < 2

= 2 < 2x < 4

= 2 + a < 2x + a < 4 + a

= 2 + a < f' (x) < 4 + a

Now f (x) is strictly increasing on (1, 2) only if f' (x) > 0 for 1 < x < 2

= 2 + a ≥ 0

= a ≥ -2

∴ Required least value of a is -2 

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अध्याय 6: Application of Derivatives - Exercise 6.2 [पृष्ठ २०६]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 6 Application of Derivatives
Exercise 6.2 | Q 14 | पृष्ठ २०६

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