Question

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

Answer 1

We have,

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

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

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

Hence, the required value of a is −2.