Using calculus, determine all maxima, \(m\) inima, and saddle points for the following unconstrained two-dimensional objective functions:

(a) \(f\left\{x_{1} x_{2}\right\}=2 x_{1}^{3}+4 x_{1} x_{2}^{2}-10 x_{1} x_{2}+x_{2}^{2}\)

(b) \(f\left\{x_{1}, x_{2}\right\}=1000 x_{1}+4 \times 10^{9} x_{1}^{-1} x_{2}^{-1}+2.5 \times 10^{5} x_{2}\)

(c) \(f\left\{x_{1}, x_{2}\right\}=\left(1-x_{1}\right)^{2}+100\left(x_{2}-x_{1}^{2}\right)^{2}\)