Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Minimum and Maximum

1. What is the difference between local minimum and absolute minimum?

2. What is the difference between local maximum and absolute maximum?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Minimum and Maximum

The minimum at the origin for y = x^2 is an absolute minimum because there are never values of y lower than the one at that point.

If you try graphing y = x^3 - 2x, you'll see it has both a local max. and a local min. But away from those points there are y values which are greater than the local max and values of y which are lower than the local min.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Minimum and Maximum

The minimum at the origin for y = x^2 is an absolute minimum because there are never values of y lower than the one at that point.

If you try graphing y = x^3 - 2x, you'll see it has both a local max. and a local min. But away from those points there are y values which are greater than the local max and values of y which are lower than the local min.

Bob

Can you show me with a graph using a different color for each local max, absolute max, local min and absolute min?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Minimum and Maximum

Will this help?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Minimum and Maximum

Will this help?

https://i.imgur.com/jWTyPeb.gif

Bob

Wow!! Beautiful graph, Bob. Thank you. Easy to understand using different colors.

Now, when we graph f(x) = -x^2, there will be an absolute maximum at the point where there graph starts to decline.

Yes?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Minimum and Maximum

Yes correct.  The diagram was getting too crowded for yet another function but, even better, you've filled in the gap.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Minimum and Maximum

Yes correct.  The diagram was getting too crowded for yet another function but, even better, you've filled in the gap.

Bob

Thank you for your motivation. On my way to an interview for a new job. Wish me luck, Bob.