Question 13337
Hi.
The diver follows a path that is a upside-down parabola
{{{graph (300,200,0,20,0,20,(-4/9)x^2+(24/9)x+12)}}}
You were right by saying the maximum point occourse when y=16.
why?
First you must find the x-value that will give a local maxima or minima of the graph.
This is just a Calculus problem
you start by taking the derivative of the function to get
(-8/9)x + (24/9) = y.
to find a local maxima you set y=0 and solve for x
(-8/9)x + (25/9) = 0.
(-8/9)x = (-25/9)
divide both sides by (-8/9 to get
x=3.
You know this will be a local maxima or minimum by this mehtod because you are setting the slope of the derivative (or tangent line to original graph) equal to zero.  All tangents after 16 will be negative because the graph is curving downward.  Also all tangents before x=3 will be positive because the graph is increasing up until this point.
I hope this helps you and doesn't confuse you.
I don't know about your calculus background.