When we use ContourPlot we see that min is at roughly T=0 and $\Phi=-175$
ContourPlot[(22500 + T^2/3) ϕ^2 +
320 ϕ^3 + ϕ^4, {T, -100, 100}, {ϕ, -250, 0},
PlotLegends -> Automatic]
We then use NMinimize
NMinimize[{(22500 + T^2/3) ϕ^2 + 320 ϕ^3 + ϕ^4, 0 < T < 100, -250 < ϕ < 0}, {ϕ, T}]
{-8.8096410^7, {$\Phi$ -> -176.125, T -> 2.9772110^-11}}
Plot3D[(22500 + T^2/3) ϕ^2 + 320 ϕ^3 + ϕ^4, {T, -100,
100}, {ϕ, -200, 20}]
When we use ContourPlot we see that min is at roughly T=0 and $\Phi=-175$
ContourPlot[(22500 + T^2/3) ϕ^2 +
320 ϕ^3 + ϕ^4, {T, -100, 100}, {ϕ, -250, 0},
PlotLegends -> Automatic]
We then use NMinimize
NMinimize[{(22500 + T^2/3) ϕ^2 + 320 ϕ^3 + ϕ^4, 0 < T < 100, -250 < ϕ < 0}, {ϕ, T}]
{-8.8096410^7, {$\Phi$ -> -176.125, T -> 2.9772110^-11}}
When we use ContourPlot we see that min is at roughly T=0 and $\Phi=-175$
ContourPlot[(22500 + T^2/3) ϕ^2 +
320 ϕ^3 + ϕ^4, {T, -100, 100}, {ϕ, -250, 0},
PlotLegends -> Automatic]
We then use NMinimize
NMinimize[{(22500 + T^2/3) ϕ^2 + 320 ϕ^3 + ϕ^4, 0 < T < 100, -250 < ϕ < 0}, {ϕ, T}]
{-8.8096410^7, {$\Phi$ -> -176.125, T -> 2.9772110^-11}}
Plot3D[(22500 + T^2/3) ϕ^2 + 320 ϕ^3 + ϕ^4, {T, -100,
100}, {ϕ, -200, 20}]
When we use ContourPlot we see that min is at roughly T=0 and $\Phi=-175$
ContourPlot[(22500 + T^2/3) ϕ^2 +
320 ϕ^3 + ϕ^4, {T, -100, 100}, {ϕ, -250, 0},
PlotLegends -> Automatic]
We then use NMinimize
NMinimize[{(22500 + T^2/3) ϕ^2 + 320 ϕ^3 + ϕ^4, 0 < T < 100, -250 < ϕ < 0}, {ϕ, T}]
{-8.8096410^7, {$\Phi$ -> -176.125, T -> 2.9772110^-11}}