-((0.6666666666666666` (r Sqrt[(
63.49604207872798` - 31.74802103936399` r +
1.1` (-2 + r)^(2/3) r)/(
63.496042078727974` - 31.748021039363987` r +
1.` (-2 + r)^(2/3) r)] (-9.` + 2 r - (
0.02309855258140601` r^3)/(-2 + r)^(1/3)) -
2 (1 - 0.034647828872109016` (-2 + r)^(2/3) - 2/r) (-2.25` r +
r^3 Sqrt[(
63.49604207872798` - 31.74802103936399` r +
1.1` (-2 + r)^(2/3) r)/(
63.496042078727974` - 31.748021039363987` r +
1.` (-2 + r)^(2/3)
r)] + (r^3 (2.2737367544323206`*^-13 (-2 + r)^(1/3) +
r (-6.349604207872807` -
1.1368683772161603`*^-13 (-2 + r)^(1/3) +
r (5.291336839894001` + (-1.0582673679787984` -
5.551115123125783`*^-17 (-2 + r)^(
2/3)) r))))/((-2 + r)^(
1/3) (63.496042078727974` + (-31.748021039363987` +
1.` (-2 + r)^(2/3)) r)^2 Sqrt[(
63.49604207872798` - 31.74802103936399` r +
1.1` (-2 + r)^(2/3) r)/(
63.496042078727974` - 31.748021039363987` r +
1.` (-2 + r)^(2/3) r)])) +
2.25` r^2 (-(0.02309855258140601`/(-2 + r)^(1/3)) + 2/
r^2 + (-4.547473508864641`*^-13 (-2 + r)^(1/3) +
r (12.699208415745616` +
2.2737367544323206`*^-13 (-2 + r)^(1/3) +
r (-10.582673679788002` + (2.116534735957597` +
1.1102230246251565`*^-16 (-2 + r)^(
2/3)) r)))/((-2 + r)^(1/3)
r (63.496042078727974` + (-31.748021039363987` +
1.` (-2 + r)^(2/3)) r)^2 Sqrt[(
63.49604207872798` - 31.74802103936399` r +
1.1` (-2 + r)^(2/3) r)/(
63.496042078727974` - 31.748021039363987` r +
1.` (-2 + r)^(2/3)
r)]))))/(-2.` + ((0.13859131548843606` +
2.` (-2 + r)^(1/3) - 0.09239421032562405` r) r)/(-2 + r)^(
1/3)))
Is there a way to find the value of $r$ where the function above is at its minimum?
I am trying to find the minimum value of the function?
How to use Mathematica to find the position of the red circle on the graph?
Thank you.
NSolve
andNMinimize
but they gave wrong result. $\endgroup$FindMinimum[fn, {r, 2.1}]
? $\endgroup$r<=2
(try evalatingfn[2]
). How do you want to treat this region? $\endgroup$