Local Minimum of x^4-9x^3+9x^2+5x-4 - Where am I Wrong?

[koudai8]

The question asks for local minimum of x^4-9x^3+9x^2+5x-4.

The answer was x=-0.21 and 5.96.

I thought 5.96 is the absolute minimum, since it gives the loweset y value on the open interval. Where am I wrong.

Thanks.

 

[ideasrule]

An absolute minimum is a local minimum; if it's a minimum across the entire interval, it's obviously a minimum locally.

 

[koudai8]

An absolute minimum is a local minimum; if it's a minimum across the entire interval, it's obviously a minimum locally.

So all absolute are also locals? Never knew that. Thanks.

 

[Dick]

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]

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.

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]

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?

Sure it is. ideasrule has it correct.

 

[koudai8]

Sure it is. ideasrule has it correct.

That's all I need. Thank you both.