Original
So, we have to find the (global) minimum of {{MATH_19}} on its domain, {{MATH_20}}.
We have to find critical points of {{MATH_21}}.
Therefore, we have to compute {{MATH_22}}.
{{CMD_23}}
{{CMD_24}}
{{MATH_25}}.
{{CMD_26}}
{{CMD_27}}
We have to find critical points of {{MATH_28}}.
So, we have to solve the equation
{{MATH_29}}.
It follows that {{MATH_30}} has the only critical point {{MATH_31}}.
{{CMD_32}}
{{CMD_33}}
Since
{{MATH_34}}, it follows that
{{MATH_35}} on {{MATH_36}} and that {{MATH_37}} on {{MATH_38}}.
This means that {{MATH_39}} is decreasing on {{MATH_40}} and increasing on {{MATH_41}}.
That means that the function {{MATH_42}} has both a local minimum and global minimum at {{MATH_43}}.
{{CMD_44}}