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Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

help! -Concavity Hints?

-3 to -1 seems to be downwards(concave) so I chose that
1 to 2 is also downward(concave)
and 2 to ∞ is downwards

Am I right?

Last edited by Mathegocart (2016-01-27 16:00:06)

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

Bob

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Registered: 2010-06-20

Posts: 10,643

Re: help! -Concavity Hints?

hi mathgogocart

I had to look up concavity as I'd not met it before.  Here's a link:

https://www.math.hmc.edu/calculus/tutor … condderiv/

You graph may be divided into 5 sections: (1) up to -3  (2)  -3 to -1   (3)  -1 to +1   (4)  +1  to +2 (5) above + 2

From that page it would seem that the function is concave upwards for (2) and (4) and concave downwards elsewhere.  Hope that helps,

Bob

ps.  The theorem only applies to open intervals as  f'' is zero at the 4 points.

pps.  If you attempt a sketch of the f' graph you will see that, for example, in the interval -3 to -1, the gradient is increasing meaning the f graph is concave upwards.

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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

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: help! -Concavity Hints?

hi mathgogocart

I had to look up concavity as I'd not met it before.  Here's a link:

https://www.math.hmc.edu/calculus/tutor … condderiv/

You graph may be divided into 5 sections: (1) up to -3  (2)  -3 to -1   (3)  -1 to +1   (4)  +1  to +2 (5) above + 2

From that page it would seem that the function is concave upwards for (2) and (4) and concave downwards elsewhere.  Hope that helps,

Bob

ps.  The theorem only applies to open intervals as  f'' is zero at the 4 points.

pps.  If you attempt a sketch of the f' graph you will see that, for example, in the interval -3 to -1, the gradient is increasing meaning the f graph is concave upwards.

Thank you!

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.