Question

The sum of the two bases and the altitude of a trapezoid is 16ft. a) Define the area A of the trapezoid as function of its altitude. b) Find the altitude for which the trapezoid has the largest possible are. (Optimization)

Answer 1

a+b+h=16

Area= h(a+b)/2= h(16-h)/2
dA/dh=0= ... you do it and solve.

Answer 2

dA/dh=(2)(1)(-1)-(h(16-h))(0)/4

dA/dh = -2

is this right?