A real valued function $f:[4, \infty) \rightarrow \mathbb{R}$ is defined as $f(x)=\left(x^2+x+1\right)^{\left(x^2-3 x-4\right)}$, then $f$ is

• A

  monotonically decreasing function
• Correct answer
  B

  monotonically increasing function
• C

  increasing in $(4,5)$ and decreasing in $(5, \infty)$
• D

  decreasing in $(4,5)$ and increasing in $(5, \infty)$

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