Question

Find the absolute extrema for the function on the given internal

Answer 1

Given the function;

`f(x)=-3x^2-24x+3`

The first derivative of the function is;

`f^(\prime)(x)=-6x-24`

At critical points;

`\begin{gathered} -6x-24=0 \\ -6x=24 \\ x=(24)/(-6) \\ x=-4 \end{gathered}`

Thus, the f(x) at x=-4 is;

`\begin{gathered} f(-4)=-3(-4)^2-24(-4)+3 \\ f(-4)=-48+96+3 \\ f(-4)=51 \end{gathered}`

Thus, the absolute maxima on the given point is;

`(-4,51)`

The absolute minima on the given points is;

`(4,-141)`