Geometrically Constructed Families of Newton's Method for Unconstrained Optimization and Nonlinear Equations

Table 3

Unconstrained optimization problems.

No.	Examples	Initial guesses	Optimum point (𝛽)
(1)	𝑥^3−6𝑥^2+9𝑥−8	2	3
		3.5
(2)	3774.522𝑥+2.27𝑥−181.529	32	40.777259826660156
		45
(3)	(𝑥−2)^2+cos(𝑥)	1	2.3542480166260
		3
(4)	𝑒^𝑥−3𝑥^2	−1	0.204481452703476
		1
(5)	10.2𝑥+6.2𝑥^3,𝑥>0	0.5	0.860541462898254
		2.0