Start the AD and mutation style extensions. Also document least squar…

[pkofod]

…es optimization and various fixes that came up while writing the nls examples.

[codecov[bot]]

Codecov Report

Attention: 93 lines in your changes are missing coverage. Please review.

Comparison is base (6fd621a) 76.91% compared to head (a4c0b0f) 75.24%. Report is 5 commits behind head on master.

:exclamation: Current head a4c0b0f differs from pull request most recent head 3ad07fc. Consider uploading reports for the commit 3ad07fc to get more accurate results

Files	Patch %	Lines
ext/ForwardDiffExt.jl	0.00%	31 Missing :warning:
ext/SparseForwardDiffExt.jl	0.00%	29 Missing :warning:
ext/AbstractDifferentiationExt.jl	0.00%	24 Missing :warning:
src/NLSolvers.jl	0.00%	6 Missing :warning:
ext/StaticArraysExt.jl	0.00%	2 Missing :warning:
src/objectives.jl	0.00%	1 Missing :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #63      +/-   ##
==========================================
- Coverage   76.91%   75.24%   -1.68%     
==========================================
  Files          54       58       +4     
  Lines        2807     2904      +97     
==========================================
+ Hits         2159     2185      +26     
- Misses        648      719      +71     

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