If the function $y=g(x)$ representing the slopes of the tangents drawn to the curve $y=3 x^4-5 x^3-12 x^2+18 x+3$ is strictly increasing then the domain of $g(x)$ is

• A

  $\left[-\frac{1}{2}, \frac{4}{3}\right]$
• B

  $\left(\frac{-1}{2}, \frac{4}{3}\right)$
• C

  $\mathbb{R}-\left(\frac{-1}{2}, \frac{3}{4}\right)$
• Correct answer
  D

  $\mathbb{R}-\left[\frac{-1}{2}, \frac{4}{3}\right]$

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