Q. 14 3.9( 43 Votes )

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

Answer :

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
⇒ a < -2x


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

 a < -2x when x ϵ [1, 2]

Now, 1 ≤ x ≤ 2
⇒ -4 ≤ -2x ≤ -2

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

a = -4

Therefore, the least value of a is -4

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