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November 15th, 2009, 09:58 AM   #1
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Help with Providing examples

Provide an example of a continuous function f:R-->R which satisfies all of the following properties

(a) non-decreasing
(b) not constant
(c) not increasing

Be sure to justify your example

I have an example as f( x ) = { 1, x<0 or x, x >= 0 with the graph that the function is constant on the left of the x axis, and increasing on the right of the x axis, but I dont know how to prove this
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November 15th, 2009, 12:47 PM   #2
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Re: Help with Providing examples

non-decreasing: f(x) = x
non constant: f(x) = x
non increasing: f(x) = -x

Justificaiton (Hints): Take the derivative

Cheers
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November 15th, 2009, 04:53 PM   #3
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Re: Help with Providing examples

Quote:
Originally Posted by gckc123
non-decreasing: f(x) = x
non constant: f(x) = x
non increasing: f(x) = -x

Justificaiton (Hints): Take the derivative

Cheers
Sorry, I forget to clarify that this is only one example that satisfies all of the conditions, I have an example as f( x ) = { 1, x<0 or x, x >= 0 this function constant on the left side of the axis, and increase on the right side of the x axis, but I dont know how to prove it.
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