Question

The function \[f(x)=x^3-3x^2+4x\], \[x\in\mathbf{R}\], is

Options

• increasing on \[\mathbf{R}\]

• constant on \[\mathbf{R}\]

• decreasing on \[(-\infty,1)\] and increasing on \[(1,\infty)\]

• decreasing on \[\mathbf{R}\]

Answer 1

For every real \[x\], \[f'(x)=3(x-1)^2+1>0\]. A positive derivative throughout \[\mathbf{R}\] implies that \[f\] is increasing on \[\mathbf{R}\].