Question 271986
Yes, there is an easier way using algebra.
Graph the given function which that shows the area (A) as a function of the width (w). A (area) is the vertical axis while w (width) is the horizontal axis.
{{{graph(400,400,-5,60,-5,660,50x-x^2)}}}
You can see from the graph that this is a parabola opening downward so there is a maximum (area) at (w, A) of (25, 625).
You can find the w coordinate of the vertex by:
{{{w = (-b)/2a}}} where: b = 50 and a = -1, so...
{{{w = (-50)/(2(-1))}}}
{{{w = 25}}}
The vertex (maximum area in this case) occurs at w = 25.