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Find the least value of a such that the function f given by {f

Question

Find the least value of a such that the function f given by $f (x) = x^{2} + a x + 1$ is strictly increasing on $(1, 2) ˙$

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Find the least value of a such that the function f given by

f (x) = x^{2} + a x + 1

is strictly increasing on

(1, 2) ˙

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Solution:

f (x) = x^{2} + a x + 1

For

f (x)

to be strictly increasing,

f^{'} (x) > 0

∴ 2 x + a > 0

\Rightarrow a > - 2 x .

It is given that

x \in (1, 2)

∴ - 2 x \in (- 4, - 2)

.
So,

a >

Maximum value of

- 2 x

∴ a > - 2

.
So, least value of

a

- 2

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Question Text	Find the least value of a such that the function f given by $f (x) = x^{2} + a x + 1$ is strictly increasing on $(1, 2) ˙$
Answer Type	Text solution:1
Upvotes	150