How do I scale an animation curve by time and value while retaining my tangent values?

I have an artist defined animationCurve that is supposed to describe how an object comes to a stop. The first key frame is at 0, 1 and the last is at 1, 0. I need to scale that curve's time by stopTime and its value by maxSpeed.

Here is a test I did:

 ///////////////////////////
 using UnityEngine;
 using System.Collections;
 
 public class AnimCurveScaleTest : MonoBehaviour {
 
     public AnimationCurve artistCurve;
     public AnimationCurve scaledCurve;
     Keyframe[] tempKeys;
     float speed = 1000f;
     float stopTime = 0.5f;
 
     // Use this for initialization
     void Start () {
         tempKeys = new Keyframe[artistCurve.length];
         for ( int i = 0; i < artistCurve.length; i++ ) {
             tempKeys[i] = new Keyframe(
                 artistCurve[i].time * stopTime,
                 artistCurve[i].value * speed,
                 artistCurve[i].inTangent,
                 artistCurve[i].outTangent
             );
         }
         scaledCurve = new AnimationCurve( tempKeys );
     }
 }
 //////////////////////////////

And this is the result: