Register to reply

Maxima-minima problems

by Kamataat
Tags: maximaminima
Share this thread:
Kamataat
#1
Dec17-04, 11:15 AM
P: 135
Hi!

For example y=-x^3-3x=0 gives y'=-3x^2-3 and setting y'=0 we get i and -i as the solutions. What does this say about the existence of the max and min points for the function y?

- Kamataat
Phys.Org News Partner Science news on Phys.org
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'
Popey
#2
Dec17-04, 11:26 AM
P: 22
Hi!

-3x2-3=0 has no solutions in real numbers

So, y' is always negative (as -3 is)
Hence, y is always decreasing (no min and max)
Kamataat
#3
Dec18-04, 04:31 AM
P: 135
ok, thanks

- Kamataat

tongos
#4
Dec18-04, 09:42 PM
P: 84
Maxima-minima problems

-x^3-3x=k

-x^3-3x-k=0=> where b makes x only have two solutions.....
x^3+3x-3x^2+k=(x^2-bx-(b/2)^2)(x+c)
x^3-bx^2-b^4/4x+x^2c-bcx-cb^4/4
k= -cb^4/4
-b+c=0
-b^4/4-b^2=-3
b^4+4b^2=12
b^4+4b^2-12=0
(b^2-h)(b^2-a)
(a+h)=-4
ah=12
crisalyn
#5
Sep17-10, 03:16 AM
P: 1
hi!
how determine whether that point is the maximum or the minimum?
Mark44
#6
Sep17-10, 09:10 AM
Mentor
P: 21,397
Quote Quote by crisalyn View Post
hi!
how determine whether that point is the maximum or the minimum?
The second derivative test is helpful. At a critical number c for which f'(c) = 0, if f''(c) > 0, (c, f(c)) is a local minimum point; if f''(c) < 0, (c, f(c)) is a local maximum point.

There's more to this, but your calculus text should have more information about the details.

In the future, if you have a question, start a new thread rather than adding onto an old thread. This thread is six years old.


Register to reply

Related Discussions
Maxima and minima Calculus & Beyond Homework 2
Maxima and Minima Calculus & Beyond Homework 2
Maxima & Minima Introductory Physics Homework 18
Maxima and Minima Problem Introductory Physics Homework 3
Applied Maxima and Minima Problems Calculus 4