Question

Find the least value of a such that the function f given is strictly increasing on [1, 2].

Answer 1

The given function f is defined as,

f( x )= x 2 +ax+1

The derivative of f is given as,

f ′ ( x )= df( x ) dx = d( x 2 +ax+1 ) dx =2x+a

The given function f will increase in the given interval ( 1,2 ) when f ′ ( x )>0, so

2x+a>0 x> −a 2

In the above expression, x∈( 1,2 ). Hence, for the least value of a we must put least value for x.

−a 2 =1 a=−2

Thus, the least value of a such that the function f is strictly increasing is −2.