The drag on an airplane traveling at velocity v is D=av^2+(b/v^2) where a and b are positive constants. At what speed does the airplane experience the least drag.

Question

I have so far that D'=-2b/v^3 do i set this equal to zero then i get 0=-2 don't think that is the right way where do i go from here

Answer 1

I get

D' = 2av - 2b/v^3
then set D'=0 to get

2av - 2b/v^3 = 0
v = ∜(b/a)

Answer 2

how do you get 2av should that be zero since a is a constant or did i miss something in class

Answer 3

a is a constant, just like b.

d/dv(av^2) = (a)(2v) = 2av

it doesn't make the whole term 0, it just multiplies. Funny you kept the b, but not the a.