The problem involves finding the local minimum of the polynomial function x^4-9x^3+9x^2+5x-4. The original poster expresses confusion regarding the distinction between local and absolute minima, particularly in relation to the values x=-0.21 and x=5.96.
Participants have engaged in clarifying the relationship between local and absolute minima. Some have confirmed that the absolute minimum is indeed a local minimum, while others are still grappling with the implications of this understanding. The discussion is ongoing with multiple interpretations being explored.
The original poster appears to be operating under the assumption that there can be a distinction between local and absolute minima, which is being questioned by other participants. There is a focus on the specific values provided in the problem and their classifications.
ideasrule said:An absolute minimum is a local minimum; if it's a minimum across the entire interval, it's obviously a minimum locally.
Dick said:You aren't wrong about x=5.96 being the absolute minimum. But the problem is asking for local minima. There's more than one.
koudai8 said:I just thought the other value is the absolute minimum, not the local minimum, so I didn't include it as the local minimum. So, the absolute is ALWAYS also a local one?
Dick said:Sure it is. ideasrule has it correct.