Problem 32 Solution

Let y be the shadow over neighbor's yard.

By similar triangles: x/(36+x²)^1/2=(x+y)/15.

y=15x/(36+x²)^1/2-x.

y^'=(((15*(36+x²)^1/2)-(15x²*(36+x²)^-1/2)) / 36+x²) - 1.

Then set y^'=0 and solve for x.

Finally subsitute x in the similar triangles formula to solve for y.