The function $f$ defined by $f\left(x\right)=x^3-3x^2+5x+7$ is:

• A

  Decreasing in $R$
• Correct answer
  B

  Increasing in $R$
• C

  Increasing in $\left(0, \infty \right)$ and decreasing in $\left(-\infty , 0\right)$
• D

  Decreasing in $\left(0, \infty \right)$ and increasing in $\left(-\infty , 0\right)$

Hence, the correct answer is option: 'B'.