SOLUTION
From the question given, the projectile follows the path
[tex]h\mleft(t\mright)=-3t^2+12t-5[/tex]At maximum height
[tex]h^{\prime}(t)=0[/tex]Hence, we will have to find the derivative of the function, and then get the time t.
[tex]\begin{gathered} h\mleft(t\mright)=-3t^2+12t-5 \\ h^{\prime}(t)=-6t+12 \\ \text{But } \\ h^{\prime}(t)=0 \\ \text{Then } \\ -6t+12=0 \\ 6t=12 \\ t=\frac{12}{6} \\ t=2 \end{gathered}[/tex]Hence the answer is t = 2
