For what values of a the function f given f (x) = x² + ax + 1 is increasing on [1, 2]?

Solution:

Increasing functions are those functions that increase monotonically within a particular domain,

and decreasing functions are those which decrease monotonically within a particular domain.

We have

f (x) = x² + ax + 1

Therefore,

f' (x) = 2x + a

Now,

the function f is strictly increasing on [1, 2]

Therefore,

⇒ f' (x) > 0

⇒ 2x + a > 0

⇒ 2x > - a

⇒ x > - a/2

Here, we have 1 ≤ x ≤ 2

Thus,

- a/2 > 1

a > - 2

Thus, for a > - 2

function f given f (x) = x² + ax + 1 is increasing on [1, 2]

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.2 Question 14

For what values of a the function f given f (x) = x² + ax + 1 is increasing on [1, 2]?

Summary:

Given that  f (x) = x² + ax + 1, hence the function is increasing on [1, 2] for all the values of  a > - 2