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May 11th, 2010, 12:19 PM   #1
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Minimum value

I don't understand the following question. So do I have to find the minimum point in the function? I can do that. But I don't understand the format the functions are written in. I'm used to the f(x)=(x^2)+5 kind of format. Can someone please help me figure out what the functions are? Thank you and I'd really appreciate your help!

For each of the following functions, determine whether or not it attains a minimum value anywhere on its domain, and if so find the minimum value and a point (on the domain) at which it is attained. Provide a brief explanation.

a) f:[-1,1]?R
x ? (x^2)-1

b) g0,1]?R
t ? t

c) h:[-6,9]?R
a ? { 3 if a=2; 2 otherwise}
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May 11th, 2010, 12:34 PM   #2
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Re: Minimum value

Quote:
Originally Posted by dk1702
...

a) f:[-1,1]?R
x ? (x^2)-1

b) g0,1]?R
t ? t

c) h:[-6,9]?R
a ? { 3 if a=2; 2 otherwise}
a) The domain is the INTERVAL [-1,1]
x --> (is mapped to) x^2 -1.
In other words, f(x) = x^2 - 1.
The minimum occurs at critical points (calculus approach) or at endpoints of the interval.

b) g(t) = t. This is like g(x) = x, just with a different letter used for in the input. Of the two (maximum and minimum), only one exists.

c) This is a piecewise function. The possible inputs are values in the interval [-6,9] (but this doesn't really matter much).
The output is 3, unless a (the input) happens to be 2... in this case the output is 3.
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May 11th, 2010, 01:25 PM   #3
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Re: Minimum value

Quote:
a) The domain is the INTERVAL [-1,1]
x --> (is mapped to) x^2 -1.
In other words, f(x) = x^2 - 1.
The minimum occurs at critical points (calculus approach) or at endpoints of the interval.

b) g(t) = t. This is like g(x) = x, just with a different letter used for in the input. Of the two (maximum and minimum), only one exists.

c) This is a piecewise function. The possible inputs are values in the interval [-6,9] (but this doesn't really matter much).
The output is 3, unless a (the input) happens to be 2... in this case the output is 3.
So I have to find the minimum value in the given domain?
Meaning: (0, -1) for a). For b) would it be (0.001, 0.001) since point (0, 0) isn't included? and how would I state c) since there are more than one points?
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May 11th, 2010, 01:54 PM   #4
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Re: Minimum value

Minimum VALUE, not "POINT".
a) The minimum value is -1. (You have correctly identified where it happens, but that it not required)

b) What about the point (.000001, .000001)? Or what about (.0000000000000000000000000001, .000000000000000000000000001) ??
If you name a VALUE, I can name one smaller. Always. Combine this with what I already said about part b), and you'll have an answer!

c) Just say the value. Sure, it happens at almost every point in the domain, but you are being asked for a value.
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May 11th, 2010, 05:58 PM   #5
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Re: Minimum value

Quote:
b) What about the point (.000001, .000001)? Or what about (.0000000000000000000000000001, .000000000000000000000000001) ??
If you name a VALUE, I can name one smaller. Always. Combine this with what I already said about part b), and you'll have an answer!
I got it. There is no minimum. Thanks!
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