I have given the marketing role the 'create new', 'edit own' and 'delete own' permission for the Article content type however when I log in with that account the 'edit' button doesn't appear on the article page so that user cannot modify the page]1
While the query you posted is vague, you can follow few below checks to debug more on this issue:- a.) Check if the logged in user has the role(Marketing) which you allowed to edit the content.
b.) Check if the node you want to edit actually belongs to that specific user.
c.) Try to access the url /node/[content-node-id]/edit manually and see if you are able to access the page. If so is the case then Check if your theme is supressing the tabs by any chance. Try by changing the theme to a different one and look for tabs.
Hope this helps :)