Mathematics

This is an optimization problem where you need to find the highest point a parabola reaches on a closed interval. Since the parabola opens downward (negative leading coefficient), the maximum will either be at the vertex or at one of the endpoints. Find the vertex using $x = -\frac{b}{2a}$, check if it lies in $[-1, 5]$, then evaluate $f(x)$ at the vertex and both endpoints to compare.

This is an optimization problem where you need to find the highest point a parabola reaches on a closed interval. Since the parabola opens downward (negative leading coefficient), the maximum will either be at the vertex or at one of the endpoints. Find the vertex using $x = -\frac{b}{2a}$, check if it lies in $[-1, 5]$, then evaluate $f(x)$ at the vertex and both endpoints to compare.