homework problems

[NGD]

1.Given three graphs which are the original function, the first derivative, and the second derivative, how can I identify which is which? 2.How can I calculate: integral from 15 to 9 of 7x^3 multiplied by x^.5 dx? 3.How can I solve optimization problems? 4.What does the third derivative tell me about a graph? 5.Why does the subject linear approximations is starting to fade away in textbooks? Thank you for answering.

 

[Steven G]

You do realize that this is not a free homework site where we do your homework. This is a help site where we help you solve your own problem with hints from the helpers on this forum.

Hints: 1) The 1st derivative will give the slopes of the original function. The 2nd derivative will give the slopes of the 1st derivative. That is just use definitions.
2) Why not do the multiplication and then integrate.

 

[NGD]

Thank you. Can you tell me how to integrate? Can you give me the answers for questions 3,4,and 5?

 

[tkhunny]

5) Is it? Prove it. Show the multiple books you have examined and demonstrate your evidence. Then, given your agreement with the premise, speculate on the causes.

 

[Steven G]

Thank you. Can you tell me how to integrate? Can you give me the answers for questions 3,4,and 5?

Sure. One way is to partition the base into n equal segments, find the height for each endpoint, multiply each height by its base and then take the limit as n approaches infinity.

 

[yoscar04]

1.Given three graphs which are the original function, the first derivative, and the second derivative, how can I identify which is which? 2.How can I calculate: integral from 15 to 9 of 7x^3 multiplied by x^.5 dx? 3.How can I solve optimization problems? 4.What does the third derivative tell me about a graph? 5.Why does the subject linear approximations is starting to fade away in textbooks? Thank you for answering.

Regarding your second question, perform the multiplication as one of the moderators suggested (multiplying power functions with same base) and then look for a function than when you perform its derivative, it gives you the function you want to integrate. Use the fundamental theorem of calculus for definite integrals to evaluate your integral between the limits you have. Question 3: you should be more specific. Question 5) Not true. There are plenty of books in numerical analysis and physics that would prove you wrong.

 

[Steven G]

Question 5) Not true. There are plenty of books in numerical analysis and physics that would prove you wrong.

There being plenty of books that talk about linear approximation means nothing. I can find many books that use log tables. Now if those books you are referring to are recent books that is another story.

 

[Dr.Peterson]

5.Why is the subject of linear approximations starting to fade away in textbooks?

I can't picture this being a homework problem, as you claim. (I've corrected the grammar.)

To determine whether it is true would require gathering a lot of data. To determine why would be an even more difficult task, unless they are asking for mere speculation. You would need to survey publishers and authors, perhaps, but even they might not have a reason.

At best, I could picture this being asked if the textbook or lecture proposed an explanation, and you are to parrot what you were taught, without thinking for yourself.

 

[yoscar04]

There being plenty of books that talk about linear approximation means nothing. I can find many books that use log tables. Now if those books you are referring to are recent books that is another story.

In the line of comments that mean nothing, last time I saw a book using log tables was 45 years ago.
No, I am not referring to those kind of books. Linear approximations are the basics of many theories, i.e. classical electromagnetic theory, and I haven't seen that people stopped writing books about Maxwell equations. Same thing regarding books on linear partial differential equations. If the author of the question was referring to log tables I guess it is indeed fading., if he is not looking for sarcasms there are a few modern math books dealing with linear approximations: 1) Eriksson, Estep and Johnson, Piecewise linear approximation (2004). 2) Abdelmalek, Malek, Numerical linear approximation in C (2008). Another one a bit more advanced: Tomas-Rodriguez, Banks, Linear approximations to non linear dynamical systems (2010).

 

[Deleted member 4993]

1.Given three graphs which are the original function, the first derivative, and the second derivative, how can I identify which is which? 2.How can I calculate: integral from 15 to 9 of 7x^3 multiplied by x^.5 dx? 3.How can I solve optimization problems? 4.What does the third derivative tell me about a graph? 5.Why does the subject linear approximations is starting to fade away in textbooks? Thank you for answering.

3.How can I solve optimization problems?

That is one of the most ridiculous question I have ever encountered! It is like asking - "How can I earn money?"

Simple answer -

work where you can contribute.

 

[Deleted member 4993]

1.Given three graphs which are the original function, the first derivative, and the second derivative, how can I identify which is which? 2.How can I calculate: integral from 15 to 9 of 7x^3 multiplied by x^.5 dx? 3.How can I solve optimization problems? 4.What does the third derivative tell me about a graph? 5.Why does the subject linear approximations is starting to fade away in textbooks? Thank you for answering.

5.Why does the subject linear approximations is starting to fade away in textbooks?

Because people are studying in the park - during rain - and the print is fading due to exposure to UV rays and getting wet and drying ......