Expert: Paul Klarreich - 12/7/2007

Question
Derivatives help to determine when a function is increasing or decreasing, concave up or concave down, at a relative maximum or minimum or at an inflection point. I would like to know about these 7 characteristics and what information from the derivatives would lead one to conclude that the characteristic holds for the function.
7 characteristics are:
Increasing, decreasing, relative maximum, relative minimum, concave up, concave down, and inflection point.
I learned calculus for 2 months and I don’t know too much about it. Please use simple words to answer the question. Thank you  

Answer
Questioner:   Abigail
Category:  Calculus
Private:  No
 
Subject:  Understanding Calculus
Question:  Derivatives help to determine when a function is increasing or decreasing, concave up or concave down, at a relative maximum or minimum or at an inflection point. I would like to know about these 7 characteristics and what information from the derivatives would lead one to conclude that the characteristic holds for the function.
7 characteristics are:
Increasing, decreasing, relative maximum, relative minimum, concave up, concave down, and inflection point.
I learned calculus for 2 months and I don’t know too much about it. Please use simple words to answer the question. Thank you
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Hi, Abigail,

Maybe 2 months wasn't enough.  Anyway, here's the clue.  You will have to look up the symbolism in your calculus book. (You DO have one, right?)

increasing:   f'(x) is +
decreasing:   f'(x) is -
relative max: f'(x) is 0 and f'' is -
relative min: f'(x) is 0 and f'' is +
concave up:  f'' is +
concave down:  f'' is -
inflection point:  f'' is 0

Now you have to do a LOT of examples.  Figure about 4 hours a day for the next month and you'll be okay.  But here's my advice -- you don't seem ready to teach it to yourself.  Find a good teacher somewhere and take the class.