Hi, I have a function question may you help me?
Which one is increasing function for all x values?
(a) y = |x - 7|
(b) y = 2x^2 + 9
(c) 3x^3 -11
(d) 4x^4 + 2 how can i prove?
Thank you
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Hi, I have a function question may you help me?
Which one is increasing function for all x values?
(a) y = |x - 7|
(b) y = 2x^2 + 9
(c) 3x^3 -11
(d) 4x^4 + 2 how can i prove?
Thank you
C (although it is neither increasing nor decreasing at x = 0)
All the other ones are decreasing for part of the domain.
You posted this in the pre-calculus forum.Quote:
Originally Posted by sunrise
Thus there is no way to prove this one way or the other.
You can simply draw the graphs and see the answer. But that is hardly a poof.
On the other hand, with calculus we can see which one has a non-negative derivative. That would prove it.
richard,
How you solved and thought that C is increasing?
Should i give value to the x?
Assigning a value to x has no indication of whether a function is increasing or not.Quote:
Originally Posted by sunrise
Why don't you just graph the function? To rigorously prove it, we note that its derivative is 9x^2, which is always non-negative. Therefore the function in (C) is always increasing (except when x = 0, where the derivative is zero).
Technically the functionQuote:
Originally Posted by richard1234
is increasing everywhere.
The the statement thatis an increasing function means that if
then
.
That is clearly true in this case. When I made the remark reply #3 about proof, it was addressing the fact that this is a precalculus forum.
There is of course a perfectly good way of proving this.
Suppose thatthen
. Proved.
If we think from your idea,
y = 2x^2 + 9 is also increasing isnt it?
Thanks
No it is not.Quote:
Originally Posted by sunriseIf we think from your idea,
is also increasing isnt it?
BUT
.
Now I understand thank you.