f'(1) = -4 + 24 -44 + 24 = 0
f'(3) = -4*27 + 24*9 -44*3 + 24
f'(3) = -108 + 216 -132 + 24 = 0
The domain of f(x)is x not equal 2
by definition.
Jim FitzSimons
--- In Math4u@yahoogroups.com, "Brian E. Jensen" <brianejensen@...>
wrote:
>
> I agree with the second Jim that f(2) exists and it is a minimum.
> I agree with the original question that if a function is
differentiable, there must be a minimum between 2 maxima. But I
think Jim FitzSimons is talented so maybe I am missing something.
> Going back to Jim FitzSimons message
> f(x)=-x*(x-4)*(x^2-4*x+6), x not equal 2
> How did Jim come up with such an example, why is this factored
and why did Jim say there are maxima at x=1 and x=3?
> f(x)= -x^4 + 8x^3 - 22x^2 + 24x
> f'(x) = -4x^3 + 24x^2 -44x + 24
> If I substitute 1 or 3 for x into the above equation, I don't
get zero so there is no maximum or minimum at x=1 or x=3
> Regards, Brian Jensen
> From: Jim
> To: Math4u@yahoogroups.com
> Sent: Sunday, September 23, 2007 11:43 AM
> Subject: [Math4u] Re: Maxima & Minima
> A different Jim disagreed with Jim FitzSimons:
> >Unless I misread your function f(2)=8 so it does exist and is a
minima.
>
> --- In Math4u@yahoogroups.com, "w7anf" <cherry@> wrote:
> >
> > False, here is an example.
> > f(x)=-x*(x-4)*(x^2-4*x+6), x not equal 2
> > f(x) has maximas at x=1 and x=3.
> > The minima should be at x=2, but the function does not exist
> > at x=2. f(x) is differentiable at x=2.
> > Jim FitzSimons
> >
> >
> > --- In Math4u@yahoogroups.com, "sanjivadayal" <sanjivadayal@>
wrote:
> > >
> > > Whether the following statement is true or false?
> > > "If f(x) is a differentiable function, then there must be at
least
> > one
> > > minima between two maximas".
>
Yahoo! Groups Links
<*> To visit your group on the web, go to:
http://groups.yahoo.com/group/Math4u/
<*> Your email settings:
Individual Email | Traditional
<*> To change settings online go to:
http://groups.yahoo.com/group/Math4u/join
(Yahoo! ID required)
<*> To change settings via email:
mailto:Math4u-digest@yahoogroups.com
mailto:Math4u-fullfeatured@yahoogroups.com
<*> To unsubscribe from this group, send an email to:
Math4u-unsubscribe@yahoogroups.com
<*> Your use of Yahoo! Groups is subject to:
No comments:
Post a Comment