Home
Class 12
MATHS
For what values of a the function f giv...

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

Text Solution

Verified by Experts

`f(x) = x^2+ax+1`
For `f(x)` to be strictly increasing, `f'(x) gt 0`.
`:. 2x+a gt 0`
`=> a gt -2x.` It is given that `x in (1,2)`.
`:. -2x in (-4,-2)`.
So, `a gt `Maximum value of `-2x`.
`:. a gt -2`.
...
Promotional Banner

Similar Questions

Explore conceptually related problems

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)dot

Prove that the function f given by f(x)=x-[x] is increasing in (0,\ 1) .

Prove that the function f given by f(x)=x-[x] us increasing in (0,1)dot

Find the least value of ' a ' such that the function f(x)=x^2+a x+1 is increasing on [1,\ 2] . Also, find the greatest value of ' a ' for which f(x) is decreasing on [1,\ 2] .

For what values of x, the function f(x)=(x + 1)^3(x - 3)^3 is increasing on R.

The maximum value of the function f(x) given by f(x)=x(x-1)^2,0ltxlt2 , is

The function f(x) = tan ^-1 x - In(1 + x^2) is increasing for

The domain of the function f given by f(x)=(x^(2)+2x+1)/(x^(2)-x-6)

Let I be any interval disjoint from (1, 1) . Prove that the function f given by f(x)=x+1/x is strictly increasing on 1.

For which values of x , the function f(x)=x/(x^2+1) is increasing and for which value of x , it is decreasing.