+26387 what is the minimum for this equation, C(x) 0.5x^2+23x-216+2600/x
Minimum c'(x) = 0
$$c'(x) = 2 * 0.5 x +23 -1*(2600)x^{-2}=x +23 -\frac{2600}{x^{2}} = 0\\
c'(x) = 0:\\
x +23 -\frac{2600}{x^{2}} = 0\\
\frac{2600}{x^{2}} = x+23\\
2600 = x^2(x+23)\\
2600 = x^3+23x^2\\
x^3+23x^2-2600=0\\
x= 9.01217 ( \mbox{ and 2 imaginary solutions} )$$
c(9.01217) = 320.38829
Minimum: (9.01217, 320.38829)
+26387 what is the minimum for this equation, C(x) 0.5x^2+23x-216+2600/x
Minimum c'(x) = 0
$$c'(x) = 2 * 0.5 x +23 -1*(2600)x^{-2}=x +23 -\frac{2600}{x^{2}} = 0\\
c'(x) = 0:\\
x +23 -\frac{2600}{x^{2}} = 0\\
\frac{2600}{x^{2}} = x+23\\
2600 = x^2(x+23)\\
2600 = x^3+23x^2\\
x^3+23x^2-2600=0\\
x= 9.01217 ( \mbox{ and 2 imaginary solutions} )$$
c(9.01217) = 320.38829
Minimum: (9.01217, 320.38829)
