Differential Equations/local extrema

Advertisement


Question
hello,

I have a question.

y=g(X)
domain all real number and differentiable every where

g'(-3)=g'(4)=g'(8)=0
g"(-3)=0
g"(4)=3
g"(8)=-6


whats the local extrema

I am confused

i think
Local Max is -6 at x=8
Local Min is 3 at x=4


but what does g'(-3)=g'(4)=g'(8)=0 means then.

Thanks
Mnsor

Answer
If f'(x) = 0, the point is a maximum, minimum, or inflection points.
If f"(x) > 0, f(x) is a local minimum.  If f"(x) < 0, f(x) is a local maximum.
If f"(x) = 0, there is an inflection point in f() at x.

Since g'(-3) = 0, g'(4) = 0, and g'8) = 0, x=-3, x=4, and x=8 are all critical points.
Since g"(-3) = 0, that means there is an inflection point in g(x) at x = -3.
Since g"(4) = 3, and 3>0, that means there is a minimum in g(x) at x = 4.
Since g"(8) = -6, and -6<0, that means there is a maximum in g(x) at x = 8.

The values of g(x) at any of these points are not given.

Differential Equations

All Answers


Answers by Expert:


Ask Experts

Volunteer


Scott A Wilson

Expertise

I am capable of solving most ordinary differential equations and a few not so ordinary, but those are few and far between.

Experience

I have taken Differential Equations at OSU. Occasionally I have assisted people with questions on the subject.

Publications
I wrote a thesis on the study of shock waves and rarefaction fans. That occurs in nature when mathematics fails to apply. See, mathematics says that when shock waves appear, there should be two solutions whereas nature knows there is only one way to be in that area. When rarefaction fans occur, the mathematics says there should be no solution, but despite this, nature still moves ahead with its own plan.

Education/Credentials
I received an MS degree at OSU in Mathemematics and a BS degree at OSU in Mathematical Science.

Awards and Honors
I graduated from OSU with a Bachelor of Science degree in mathematics with honors. Two years later, I graduated from OSU with a Master of Science degree in mathematics with honors. Between these two degrees, I have more hours in graduate courses that required to get them.

Past/Present Clients
I answered many questions at OSU, down in south seattle at a college, at a church in Corvallis, OR, as Safeway in Washington, and many other areas. I have answered over 8,500 right here, but only a little over 190 of them have been in differential equations.

©2016 About.com. All rights reserved.