Our function is a parabola, therefore, it has only one critical point which is its vertex. Since the coefficient of the squared term is negative, the vertex is the maximum point.The critical points of a function are given by the zeros of the first derivative. The first derivative of our function is:
[tex]f^{\prime}(x)=-6x-18[/tex]
The solutions for the following equation are the critical points of the original function:
[tex]-6x-18=0\implies x=-3[/tex]
The maximum point happens at x = - 3.
To find the corresponding value, we just have to evaluate x = - 3 into our function:
[tex]f(-3)=-3(-3)^2-18(-3)-26=1[/tex]
The maximum value of the function is 1, and it occurs at x = - 3.
