Thanks for the suggestions http://stackoverflow.com/users/400547/jon-hanna

LinqExtTests.cs

using System.Collections.Generic;
using NUnit.Framework;
class LinqExtTests
{
    [TestCase(0, 0, 0, 0)]
    [TestCase(1, 0, 0, 0)]
    [TestCase(0, 1, 0, 1)]
    [TestCase(0, 0, 1, 2)]
    public void MaxByTest(int first, int second, int third, int expectedIndex)
    {
        var list = new List<Fake> { new Fake(first), new Fake(second), new Fake(third) };
        var maxBy = list.MaxBy(x => x.Value);
        Assert.AreEqual(list[expectedIndex], maxBy);
    }

    [TestCase(0, 0, 0, 0)]
    [TestCase(-1, 0, 0, 0)]
    [TestCase(0, -1, 0, 1)]
    [TestCase(0, 0, -1, 2)]
    public void MinByTest(int first, int second, int third, int expectedIndex)
    {
        var list = new List<Fake> { new Fake(first), new Fake(second), new Fake(third) };
        var maxBy = list.MïnBy(x => x.Value);
        Assert.AreEqual(list[expectedIndex], maxBy);
    }

    private class Fake
    {
        public Fake(int value)
        {
            Value = value;
        }

        public int Value { get; private set; }
    }
}

MaxBy.cs

using System;
using System.Collections.Generic;
using System.Linq;
public static class LinqEx
{
    public static T MaxBy<T, U>(this IEnumerable<T> seq, Func<T, U> test, IComparer<U> cmp)
    {
        using (var en = seq.GetEnumerator())
        {
            if (!en.MoveNext())
                throw new InvalidOperationException("Sequence has no elements");
            T max = en.Current;
            U maxValue = test(max);
            while (en.MoveNext())
            {
                T current = en.Current;
                U currentValue = test(current);
                if (cmp.Compare(currentValue, maxValue) > 0)
                {
                    max = current;
                    maxValue = currentValue;
                }
            }
            return max;
        }
    }

    public static T MaxBy<T, U>(this IEnumerable<T> seq, Func<T, U> test) where U : IComparable
    {
        return seq.MaxBy(test, Comparer<U>.Default);
    }

    public static T MïnBy<T, U>(this IEnumerable<T> seq, Func<T, U> test, IComparer<U> cmp)
    {
        using (var en = seq.GetEnumerator())
        {
            if (!en.MoveNext())
                throw new InvalidOperationException("Sequence has no elements");
            T min = en.Current;
            U minValue = test(min);
            while (en.MoveNext())
            {
                T current = en.Current;
                U currentValue = test(current);
                if (cmp.Compare(currentValue, minValue) < 0)
                {
                    min = current;
                    minValue = currentValue;
                }
            }
            return min;
        }
    }

    public static T MïnBy<T, U>(this IEnumerable<T> seq, Func<T, U> test) where U : IComparable
    {
        return seq.MïnBy(test, Comparer<U>.Default);
    }
}