Ash's 5th post

After a very interesting day involving newborn guppy fish, I yawn and crawl in bed...almost asleep...until I realize...I FORGOT MY CALCULUS BLOG! =0 *freak out*

Okay...soooo, what I understood most this week was on the study guide...the one with all of the answers...yes, very sad, I know.

Anyway, numbers 124 and 125, I FINALLY understand after someone explained them ever so slowly. Since these require graphs, I guess I'll make some on paint ^^

Number 124 on the Multiple Choice Study Guide With Answers
Note: Sorry for all of the links, but it was much easier for me to see things step by step. Also, it's not perfect, please just pretend it is. The lines are only the even numbers.

The graph of F is shown below. On what interval is F' an increasing function?
http://i153.photobucket.com/albums/s225/Inutaisho_lover/th_Original.jpg
a) (2, ∞)
b) (0, ∞)
c) (-2, ∞)
d) (-4, ∞)
e) (1, ∞)


1) Find your zeros and mark them. (Red dots on graph) http://i153.photobucket.com/albums/s225/Inutaisho_lover/th_1.jpg

2) Mark your minimums and maximums. (Green dots on graph) http://i153.photobucket.com/albums/s225/Inutaisho_lover/th_2-1.jpg

3) Bring your minimums and maximums down to y=0. (Pink arrows on graph) http://i153.photobucket.com/albums/s225/Inutaisho_lover/th_3.jpg

4) The graph is that of a cubic and you know the derivative of a cubic is a parabola, right? (Because (this is an example, NOT the equation of the graph) f(x)=3x^3 and f'(x)=6x^2) This step was to figure that out.

Now here comes the really hard part for me to explain because I don't know HOW to explain what I do.

5) When going left to right, the first line is increasing right? The derivative of that is decreasing. So, draw a line decreasing THROUGH y=0 AT x=-4. ( Blue line on graph) http://i153.photobucket.com/albums/s225/Inutaisho_lover/th_5.jpg

6) For your minimum, I was told to just estimate it. (Light blue curve on graph) http://i153.photobucket.com/albums/s225/Inutaisho_lover/th_6-1.jpg

7) Now, since the next line (when going left to right) is decreasing, the derivative is to increase. (Dark blue line on graph...also, it's very crooked, please ignore that) http://i153.photobucket.com/albums/s225/Inutaisho_lover/th_7-1.jpg

8) Because the derivative of a cubic is a parabola, you're finished graphing!

9) Just look at your graph to see what is increasing, which happens to be c) (-2, ∞)

Hope that helps! Sorry for the horrible graphs and many links.

Ohh, as for my question, can someone explain how to find the equation of a graph. I completely forgot this and I can't find my Advanced Math notebook (if you saw my room, you'd know why). Also, the power point project is due the 28th right?