iControl - fetching LTM profile config - how to know values are inherited from parent profile

Are you referring to the "Parent Profile" field in GUI or the "defaults-from" attribute in tmsh? If so, it is named "detaultsFrom" in iControl REST (camel case naming convention). You should be able to see it. The following example retrieves this field from the profile 'httpTest' which is from the http profile.

curl -sku admin:<passwd> https://<host>/mgmt/tm/ltm/profile/http/httpTest?\$select=defaultsFrom

This httpTest has "Insert X-Forwarded-For" enabled and that's the only parameter that is different from the parent "http". You can see that only this field is different and other parameters are identical from the following test (obviously, name, defaultsFrom or any properties that are intrinsic to the profiles are different).

curl -sku admin:<passwd> https://<host>/mgmt/tm/ltm/profile/http/http | python -m json.tool > http
curl -sku admin:<passwd> https://<host>/mgmt/tm/ltm/profile/http/httpTest | python -m json.tool > before
diff http before
5c5,8
<     "defaultsFrom": "none",
---
>     "defaultsFrom": "/Common/http",
>     "defaultsFromReference": {
>         "link": "https://localhost/mgmt/tm/ltm/profile/http/~Common~http?ver=14.1.0.1"
>     },
47,48c50,51
<     "fullPath": "http",
<     "generation": 1,
---
>     "fullPath": "httpTest",
>     "generation": 22,
57c60
<     "insertXforwardedFor": "disabled",
---
>     "insertXforwardedFor": "enabled",
61c64
<     "name": "http",
---
>     "name": "httpTest",
69c72
<     "selfLink": "https://localhost/mgmt/tm/ltm/profile/http/http?ver=14.1.0.1",
---
>     "selfLink": "https://localhost/mgmt/tm/ltm/profile/http/httpTest?ver=14.1.0.1",

Or am I missing the point? Will you be able to show what you had performed and observed?

Thanks