Calculus Questions!

[85 Cutlass Brougham]

I am having problems learning Calculus right now, and am working on a take home test. I have no idea how to figure out "points of inflection", or how to find the maximum error possible in an area problem involving differentials.

The problem I have with the points of inflection is that they come from the second derivative test, but so does the determination of concavity. What is the difference, and how do you get each number? The problem has intervals of concavity as it's first part then it asks you to find the points of inflection. If the two are related, how?

The Differential problem states " The measurement of the edge of a piece of square floor is found to be 12 inches square with a possible error of 0.02 inches.

a. Use differentials to approximate the maximum possible error in the area of the tile.

b. Use your answer from part a to estimate the relative error

c. use the answer in part b to estimate the percentage error.

Unfortunately, my book is far from easy to understand. Plus, my lack of sleep (and confusion about other things in my life right now) means I have a difficult time reasoning through all of it. Anyone who actually knows how to go about this is welcome to post it.

 

[smallblockwagon]

I think I know this one.....









































































Is the answer Blue??? :wink:

 

[mhamilton]

The problem I have with the points of inflection is that they come from the second derivative test, but so does the determination of concavity. What is the difference, and how do you get each number? The problem has intervals of concavity as it's first part then it asks you to find the points of inflection. If the two are related, how?

It's been many years since I've done this, but was just looking over my old Calc book. Concavity and points of inflection are definitly related.

Both use the 1st (f') and 2nd derivitave (f'') of the function (f).

For concavity:
* if f'' is greater than 0 and and f' is increasing, it is concave upward.
* if f'' is less than zero and f' is decreasing, it is concave downward.

Points of inflection occur when f'' = 0, or when f is not differentiable at the point in question.

Unfortunately, I'm not really sure how to apply these theorems to your question on the tiles. When I did this, it was purely academic, e.g. given a curve, find the concavity and POI.

I hope this helps somewhat,
-Michael

 

[85 Cutlass Brougham]

Well, I just got the test back, and I got a 35% on it... I can drop the lowest test, and pray to God this is the one! I am passing otherwise.

 

[srercrcr]

The circumference is one pizza pie X 3.14.