Given the function
[tex]\begin{gathered} f(x)=-6x^2-60x-96 \\ f^{\prime}(x)=-12x-60 \end{gathered}[/tex]
The second derivative of the function is obtained as
[tex]\begin{gathered} f^{\doubleprime}(x)=-12 \\ \end{gathered}[/tex]
Since the f''(x) is negative, the function has a maxima.
At the critical point, f'(x)=0. Thus,
[tex]\begin{gathered} f^{\prime}(x)=-12x-60 \\ -12x-60=0 \\ x=-5 \end{gathered}[/tex]
Substitute the value of x in the function, to obtain y.
[tex]\begin{gathered} y=-6x^2-60x-96 \\ y=-6(-5)^2-60(-5)-96 \\ y=54 \end{gathered}[/tex]
Thus, we obtain a relative maxima at (-5,54)
There is no relative minimum.
