missile homing script issues

Hello guys! I use script below for making missile homing:

transform.LookAt(closest.transform);
transform.Translate(Vector3.forward*speed*1);

it works, but it change his direction not so smooth like i need it (look at the img below), is there some way to make it more smooth? Like the red arrow on the img below? Thanks in advance!

6634-trail.jpg

rotationSpeed = 1.0f;
movingSpeed = 2.0f;

//Smoothing Rotation
Quaternion rot = transform.rotation;
transform.lookAt(closest.transform);
transform.rotation = Quaternion.Lerp( rot, transform.rotation, rotationSpeed * Time.deltaTime );

//Smoother motion
transform.Translate(Vector3.forward * movingSpeed * Time.deltaTime);

My code from a previous project.