Math Is Fun Forum

Marakos

Guest

Concave Up Down, HELP

Hi, I need help in clarifying something.

1. When we need to find Wherther the function in Increasing or Decreasing, do we look for a 1st derivative to be "0" or DNE??? or its must be either or?

2. When we look for Inflection points in 2nd derivative, does it have to equal "0" or DNE or it can equal any of those?

3. When we look for Concavity (up,down) Does the 2nd derivaitive must equal "0" or DNE????

Because I know that to find Local Extremas 2nd derivaitve must equal Only "0" NOT Does not exist

****DNE= Does Not Exist"

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Concave Up Down, HELP

A function is increasing if f'(x) > 0.  It is decreasing if f'(x) < 0.  In order to find the intervals where f'(x) is increasing, we first look for all the points where:

(i) f'(x) = 0

OR

(ii) f'(x) has a discontinuity

Note that it is very possible for f'(x) to exist and have a discontinuity, but certainly any place where f'(x) does not exist will also be a discontinuity.  Once you've found these points, they will be the intervals where f'(x) is either greater than or less than 0.  Now all you need to do is test a point in each one of these.

Concavity is exactly the same except we're now using f''(x).

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."