diff --git a/base/range.jl b/base/range.jl
index 5c7c043a4f85e..ea67d266cdd82 100644
--- a/base/range.jl
+++ b/base/range.jl
@@ -577,20 +577,35 @@ maximum(r::AbstractUnitRange) = isempty(r) ? throw(ArgumentError("range must be
 minimum(r::AbstractRange)  = isempty(r) ? throw(ArgumentError("range must be non-empty")) : min(first(r), last(r))
 maximum(r::AbstractRange)  = isempty(r) ? throw(ArgumentError("range must be non-empty")) : max(first(r), last(r))
 
+"""
+    argmin(r::AbstractRange)
+
+Ranges can have multiple minimal elements. In that case
+`argmin` will return a minimal index, but not necessarily the
+first one.
+"""
 function argmin(r::AbstractRange)
     if isempty(r)
         throw(ArgumentError("range must be non-empty"))
     elseif step(r) > 0
         firstindex(r)
     else
-        lastindex(r)
+        first(searchsorted(r, last(r)))
     end
 end
+
+"""
+    argmax(r::AbstractRange)
+
+Ranges can have multiple maximal elements. In that case
+`argmax` will return a maximal index, but not necessarily the
+first one.
+"""
 function argmax(r::AbstractRange)
     if isempty(r)
         throw(ArgumentError("range must be non-empty"))
     elseif step(r) > 0
-        lastindex(r)
+        first(searchsorted(r, last(r)))
     else
         firstindex(r)
     end
diff --git a/test/ranges.jl b/test/ranges.jl
index eb5239aba378d..8f726a09565dd 100644
--- a/test/ranges.jl
+++ b/test/ranges.jl
@@ -1213,6 +1213,10 @@ end
         @test imax === argmax(r)
         @test extrema(r) === (r[imin], r[imax])
     end
+
+    r = 1f8-10:1f8
+    @test_broken argmin(f) == argmin(collect(r))
+    @test_broken argmax(f) == argmax(collect(r))
 end
 
 @testset "OneTo" begin
diff --git a/test/sorting.jl b/test/sorting.jl
index 4559deddd3fd0..aa7b8f4386eaf 100644
--- a/test/sorting.jl
+++ b/test/sorting.jl
@@ -173,6 +173,11 @@ end
 
             end
         end
+        @testset "issue ##34408" begin
+            r = 1f8-10:1f8
+            # collect(r) = Float32[9.999999e7, 9.999999e7, 9.999999e7, 9.999999e7, 1.0e8, 1.0e8, 1.0e8, 1.0e8, 1.0e8]
+            @test_broken searchsorted(collect(r)) == searchsorted(r)
+        end
     end
 end
 # exercise the codepath in searchsorted* methods for ranges that check for zero step range