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

It is given that function f(x) = x² + ax + 1

f’(x) = 2x + a

Now, function f will be increasing in (1,2) ,

if f’(x) >0 in (1,2)

⇒ 2x +a > 0

⇒ 2x > -a

⇒ x >

Therefore, we have to find the least value of a such that

⇒ x > when x ϵ (1,2)

⇒ x > ( when 1 < x < 2)

Therefore, the least value of a for f to be increasing on (1,2) is given by

-a/2 = 1

⇒ a = -2

Therefore, the least value of a is -2.