The critical numbers are the maximum or minimum points.
To find the maximum and minimum points, take the derivative equal to 0 then solve for the values of x.
From the problem, we have :
[tex]\begin{gathered} f(x)=6x^2-9x \\ \text{Take the derivative} \\ f^{\prime}(x)=2(6x)-9 \\ f^{\prime}(x)=12x-9 \\ \text{Equate to 0 and solve for x} \\ 0=12x-9 \\ -12x=-9 \\ x=\frac{-9}{-12} \\ x=\frac{9}{12}=\frac{3}{4} \end{gathered}[/tex]
ANSWER :
x = 3/4
