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Newton
'
s
Method
is
a
calculus
-
based
technique
to
find
the
roots
of
a
function
''
where
the
function
equals
zero
.
It
starts
with
a
guess
and
repeatedly
applies
a
formula
to
get
closer
to
the
root
.
It
uses
the
function
'
s
slope
(
derivative
)
to
improve
each
guess
.
It
'
s
effective
for
smooth
''
continuous
functions
but
can
fail
for
functions
with
no
derivative
''
flat
slopes
''
or
multiple
roots
near
each
other
.
It
'
s
great
for
precise
''
math
-
heavy
problems
but
not
for
erratic
or
non
-
differentiable
functions
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Gradient
Descent
is
a
method
used
to
find
the
minimum
of
a
function
.
Imagine
walking
downhill
towards
the
lowest
point
in
a
valley
—
that
'
s
what
this
method
does
mathematically
.
It
calculates
the
gradient
(
the
slope
)
of
the
function
and
takes
steps
in
the
direction
that
decreases
the
function
'
s
value
.
It
'
s
powerful
for
optimizing
in
machine
learning
and
economics
.
However
''
it
struggles
with
functions
having
many
valleys
(
local
minima
)
or
plateaus
''
and
might
not
find
the
absolute
lowest
point
(
global
minimum
).
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