Release api-core 1.4.0 (#5922)

Author: theacodes

CHANGELOG.md

@@ -4,6 +4,13 @@
 
 [1]: https://pypi.org/project/google-api-core/#history
 
+## 1.4.0
+
+### Dependencies
+
+- Add support for gRPC connection management (available when using optional grpc_gcp dependency) ([#5553](https://github.com/GoogleCloudPlatform/google-cloud-python/pull/5553)) ([#5904](https://github.com/GoogleCloudPlatform/google-cloud-python/pull/5904))
+- Update classifiers to drop Python 3.4 and add Python 3.7 ([#5702](https://github.com/GoogleCloudPlatform/google-cloud-python/pull/5702))
+
 ## 1.3.0
 
 ### New Features