Draw a diagram. Let
x = length of ladder
z = distance from fence to base of ladder
z/√(b^2+z^2) = (z+d)/x
xz = (z+d)√(b^2+z^2)
x = (z+db^2)√(b^2+z^2)/z
dx/dz = (z^3-db^2)/(z^2 √(b^2+z^2))
dx/dz=0 when z^3 = db^2
Use that to evaluate x
A ladder is intended to reach the wall of a building, but it must clear a fence with the length of d that stands at the distance b from
that wall. Find the shortest length of ladder required to arrange this.
note use differential calculus
1 answer