Shown in the figure below is a function and its tangent line at x = x 0 {\displaystyle x=x_{0}} .
The tangent line intersects the x {\displaystyle x} axis at the point x = x 1 {\displaystyle x=x_{1}} . The coordinate of the point x 1 {\displaystyle x_{1}} is
(a) x 1 = x 0 + f ( x 0 ) f ′ ( x 0 ) {\displaystyle x_{1}=x_{0}+{\frac {f(x_{0})}{f'(x_{0})}}}
(b) x 1 = x 0 − f ′ ( x 0 ) ( x − x 0 ) {\displaystyle \displaystyle x_{1}=x_{0}-f'(x_{0})(x-x_{0})}
(c) x 1 = x 0 − f ′ ( x 1 ) f ( x 1 ) {\displaystyle x_{1}=x_{0}-{\frac {f'(x_{1})}{f(x_{1})}}}
(d) x 1 = x 0 + f ′ ( x 1 ) f ( x 1 ) {\displaystyle x_{1}=x_{0}+{\frac {f'(x_{1})}{f(x_{1})}}}
(e) x 1 = x 0 − f ( x 0 ) f ′ ( x 0 ) {\displaystyle x_{1}=x_{0}-{\frac {f(x_{0})}{f'(x_{0})}}}
.
axis at the point 
. The coordinate of the point 
is
