[Math4u] Re: Maxima & Minima

A friend said if a function is differentiable, then it
continuous. My example is not continuous, so it is not
differentiable. I will have to find another example.
Jim FitzSimons

--- In Math4u@yahoogroups.com, "w7anf" <cherry@...> wrote:
>
> f'(x) = -4x^3 + 24x^2 -44x + 24
> 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:

http://docs.yahoo.com/info/terms/