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November 23rd, 2014, 04:32 AM   #1
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Help with this minimum...

When I enter x^4 - 2x^3 into WA, it says there is a global minimum at x = 3/2 (http://www.wolframalpha.com/input/?i=x^4+-+2x^3). The book I got this problem from says that it is a local minimum. Which is the correct answer, is it just a local minimum or is it global?

Thanks.

There's also a bonus question: how do I sketch it? The shape of the graph looks hugely different when I look at it between different values of x.

Last edited by 3uler; November 23rd, 2014 at 04:48 AM.
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November 23rd, 2014, 06:09 AM   #2
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Originally Posted by 3uler View Post
When I enter x^4 - 2x^3 into WA, it says there is a global minimum at x = 3/2 (http://www.wolframalpha.com/input/?i=x^4+-+2x^3). The book I got this problem from says that it is a local minimum. Which is the correct answer, is it just a local minimum or is it global?

Thanks.

There's also a bonus question: how do I sketch it? The shape of the graph looks hugely different when I look at it between different values of x.
It is a local minimum, and a global minimum, a global minimum is always a local minimum.

The curve comes down from +infinity as x goes from -infinity to zero, where the function has a triple root (so flattens out as it crosses the x-axis), it then decreases again to its minimum at x=3/2 from where it increases towards + infinity crossing the x axis again at x=2.

CB
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November 23rd, 2014, 06:52 AM   #3
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Originally Posted by CaptainBlack View Post
It is a local minimum, and a global minimum, a global minimum is always a local minimum.

The curve comes down from +infinity as x goes from -infinity to zero, where the function has a triple root (so flattens out as it crosses the x-axis), it then decreases again to its minimum at x=3/2 from where it increases towards + infinity crossing the x axis again at x=2.

CB
I know a global minimum is a local minimum too. That's why I said is it "just a local". Thanks for the reply, I appreciate it.
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November 23rd, 2014, 07:08 AM   #4
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I know a global minimum is a local minimum too. That's why I said is it "just a local". Thanks for the reply, I appreciate it.
If you are expected to find it by differentiating and equating the derivative to zero, then all you can say is that you have found a local minimum (maximum). You have to have additional knowledge to say if it is a global extremum or not.

So if the excise is to find the zeros of the derivative and classify them into maximum, minimum and points of inflection, the answer will be local xxxx, because that is what the method tells you.

CB
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