Given the function;
[tex]f(x)=-4x^2-32x-60[/tex]The maximum value of a function is the place where a function reaches its highest point, or vertex, on a graph. If a quadratic function has a negative "a" term, it will also have a maximum value.
Thus, the function has a maximum value.
Also;
[tex]\begin{gathered} f^{\prime}(x)=(-4\times2)x^{2-1}-(32\times1)x^{1-1} \\ f^{\prime}(x)=-8x-32 \end{gathered}[/tex]At maximum value, the derivative is zero. Thus;
[tex]\begin{gathered} -8x-32=0 \\ -8x=32 \\ x=\frac{32}{-8} \\ x=-4 \end{gathered}[/tex]Then,
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