Question

Prove that the function given by is increasing in R .

Answer 1

The given function f( x ) is defined as,

f( x )= x 3 −3 x 2 +3x−100

The derivative of the function f( x ) is given as,

f ′ ( x )= df( x ) dx = d( x 3 −3 x 2 +3x−100 ) dx =3 x 2 −6x+3 =3 ( x−1 ) 2

For the given interval x∈R,

3 ( x−1 ) 2 >0

Hence, f ′ ( x )>0.

As f ′ ( x )>0, then the given function f( x ) is increasing in R.