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]` .

Explanation

`f'(x)=2x+a`

Now, function f will be increasing in `(1, 2)`, if `f'(x)>0` in `(1, 2)`.

`f'(x)>0=>2x+a>0`

`x> -a/2`

Therefore, we have to find the least value of a such that Thus, `x> -a/2`, when `x in (1, 2)`

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

`-a/2=1=>a=-2`