First
http://postimg.org/image/60ozj4q6b/
Second question
http://postimg.org/image/vmj4o71w1/

This was not what we suggested... we suggested that you do the derivatives/integrals by hand... how you evaluate the equation is up to you, but the calculus part should be done by hand first

So for the first one, do I basically just take the numerator and divide it by the f(1,2,3)^2? Looks like that's all you did.



Well I just now started learning about derivatives in my class. I haven't taken math in a very long time and I never took calculus in high school. Doing derivatives on the calculator right now seems easier because I really don't understand the concept of a derivative right now.

The derivative is just the slope of a line.

f(x)=2x

from algebra, we know that form for a straight line is y=mx+b, and in this case m=2

when you get to higher order polynomials such as

f(x)=3*x^2+2x

the slope is not a constant 2, but now depends where you are.

so the derivative f'(x)=3/2*x+2

each term can be taken independently and is of the form

f(x)=x^n

f'(x)=x^(n-1)/n

there are also other rules, but these are the basics for a derivative. If you do no understand the concept, i HIGHLY recommend to read up on it more and perhaps watch a few videos on khan academy. This is the basis for ALL calculus later, and a strong understand is the most important.

Also, go back to the basics of using your dx and taking limits as dx goes to 0

This is not all correct your referring to the chain rule. A derivative is simply the slope of a tangent line of a function at a specific point. This is why calculus is all based on rates of change.
The biggest rule in calculus is the Chain Rule which is what your referring to but your doing it incorrectly.
Let f(x)=ax^n
Then f'(x)= n*ax^(n-1)

Ie: f(x)= 2x
Then f'(x)= 1*2x^(1-1)=2x^0=2

The rule follows for any order polynonial regardless of degree so we see
f(x)=3x^5+2x^2 then f'(x)=5*3x^(4)+2*2x^1=15x^4+4x

Got my first exam tomorrow and I'm pretty nervous. If you guys can help me understand these problems I'd appreciate it!

1: I know the slope form, but how do I find the second set of points?
http://i.imgur.com/F0Xng4s.png

2: I know how to do the other answers, how do I predict the future number? (I circled the problem)
http://i.imgur.com/3Nqeskn.png

3: How do I do part B?
http://i.imgur.com/dNLsFQh.png

Thanks!

1. This is simple the tangent line is The pink line so simply use the point given (-2,2) and pick another point on that line (2,3) for instance and calculate slope of 1/4.

2. We can see our last trend of increase is 400 over 10 years from 95 to 2005. They want to know his much of an increase to 2009 so use your slope to estimate. Slope from 95-2005 is 400/10 or 40 per year so for 4 years from 05-09 we will have an increase of 40*4 if trends continue.

3. Basic algebra it tells you to build eq which you did correctly in which y is # of shopping centers starting in year 0 which is 1999. asks you what year (x) your shopping malls (y) will reach 80,000. Plug in 80,000 for y and solve for x which is # years from year 0 (1999)

This post was edited by Xx Shin3d0wn xX on Feb 13 2015 09:03pm

Awesome!

Few questions.

1. How do I determine which set of points are x1, x2 and y1, y2? For the point intercept form.

2. I don't get this. I'm not seeing the increase that you are predicting.

3. So 80,000=1999x?

1. Using your slope equation is simply y2-y1/x2-x1
You have infinity points (x,y) points that lie on a line I just picked two (-2,2) (2,3) you'll notice if you calculate slope it doesn't matter which point you use as (X1,y1) and (x2,y2) as long as you use formula correctly.



3. No you use your equation you built in part a.

Y=684.2x+41218 Where x is # years since 1999 and y is number of hotels

Want to know what year there are 80,000 hotels? Then plug in for y and solve.
80,000=684.2x+41218 and solve for x to get the number for years since 1999.

For the second question your correct I didn't read it all it says average rate of change for century continues. So you just compute slope using points (1905,1006) and (2005,1129) to compute slope for avg change over century. Then do slope which is average change per year and multiple by number of years from 2005 to 2009 to find estimated population in 2009.
The math here is simple slope is 123/100=1.23
So 1.23*4=4.29
4.29+1129=1,133.92 which is in thousands so
1,133,920


Edit: I'm doing all of this on my phone so excuse any typos. This is all basic algebra using slopes, really confused on why this is covered in a calculus course.

This post was edited by Xx Shin3d0wn xX on Feb 13 2015 09:21pm