The graph of $\displaystyle {f{{\left({x}\right)}}}={2}{x}^{{3}}+{12}{x}^{{2}}-{72}{x}+{23}$ has two horizontal tangents.

What is the negative value of $\displaystyle {x}$ where a horizontal tangent occurs? Preview Question 6 Part 1 of 2  

What is the positive value of $\displaystyle {x}$ where a horizontal tangent occurs? Preview Question 6 Part 2 of 2