Update FAQ.md

docs/src/basics/FAQ.md

@@ -1,3 +1,38 @@
 # Frequently Asked Questions
 
-Ask more questions.
+## How is the performance of Julia's NonlinearSolve.jl vs MATLAB's fzero?
+
+This is addressed in a [Twitter thread with the author of the improved fzero](https://twitter.com/ChrisRackauckas/status/1544743542094020615).
+On the test example:
+
+```julia
+using NonlinearSolve, BenchmarkTools
+
+N = 100_000;
+levels = 1.5 .* rand(N);
+out = zeros(N);
+myfun(x, lv) = x * sin(x) - lv
+
+function f(out, levels, u0)
+    for i in 1:N
+        out[i] = solve(NonlinearProblem{false}(NonlinearFunction{false}(myfun),
+                u0, levels[i]), Falsi()).u
+    end
+end
+
+function f2(out, levels, u0)
+    for i in 1:N
+        out[i] = solve(NonlinearProblem{false}(NonlinearFunction{false}(myfun),
+                u0, levels[i]), NewtonRaphson()).u
+    end
+end
+
+@btime f(out, levels, (0.0, 2.0))
+@btime f2(out, levels, 1.0)
+```
+
+MATLAB 2022a achieves 1.66s. Try this code yourself: we receive 0.06 seconds, or a 28x speedup.
+This example is still not optimized in the Julia code and we expect an improvement in a near
+future version.
+
+For more information on performance of SciML, see the [SciMLBenchmarks](https://github.com/SciML/SciMLBenchmarks.jl)