rails 3 link_to not working - no route matches

I am working on a rails 3 app. I am trying to make a simple link_to block, but I keep getting a routing error. I am not used to rails 3 (only have used rails 4), and am wondering if I am just missing something dumb, or if this is a rails version thing.

Here are my routes

namespace :api do 
  resources :multiple_prospects, :only => [:update, :destroy] do
    put :flag,          :on => :member
    put :mass_flagging, :on => :collection
    put :mass_archived, :on => :collection
    put :mass_updating, :on => :collection
  end
end

the controller looks like this

class Api::MultipleProspects < ApiController

  def update
  end

  def flag
  end

  def destroy
  end
end

and here is the link_to that is resulting in the error: No route matches {:action=>"flag", :controller=>"api/multiple_prospects"}

<%= link_to flag_api_multiple_prospect_path do %>
   <button><i class="icon icon-flag prospect-flag"></i></button>
 <% end %>

and the output of rake routes CONTROLLER=api/multiple_prospects is

 flag_api_multiple_prospect PUT    /api/multiple_prospects/:id/flag(.:format)      api/multiple_prospects#flag
mass_flagging_api_multiple_prospects PUT    /api/multiple_prospects/mass_flagging(.:format) api/multiple_prospects#mass_flagging
mass_archived_api_multiple_prospects PUT    /api/multiple_prospects/mass_archived(.:format) api/multiple_prospects#mass_archived
mass_updating_api_multiple_prospects PUT    /api/multiple_prospects/mass_updating(.:format) api/multiple_prospects#mass_updating
               api_multiple_prospect PUT    /api/multiple_prospects/:id(.:format)           api/multiple_prospects#update
                                     DELETE /api/multiple_prospects/:id(.:format)           api/multiple_prospects#destroy

does anyone see something wrong I am doing? I have done something like this in rails 4 and it worked fine. I am not sure what I am doing wrong here that is causing this error. Any help would be much appreciated.