Given the function;
[tex]f(x)=-3x^2-24x+3[/tex]
The first derivative of the function is;
[tex]f^{\prime}(x)=-6x-24[/tex]
At critical points;
[tex]\begin{gathered} -6x-24=0 \\ -6x=24 \\ x=\frac{24}{-6} \\ x=-4 \end{gathered}[/tex]
Thus, the f(x) at x=-4 is;
[tex]\begin{gathered} f(-4)=-3(-4)^2-24(-4)+3 \\ f(-4)=-48+96+3 \\ f(-4)=51 \end{gathered}[/tex]
Thus, the absolute maxima on the given point is;
[tex](-4,51)[/tex]
The absolute minima on the given points is;
[tex](4,-141)[/tex]
