October 11, 2006

Post: Day 22

1) The graph of f ' is shown:a)Where is f increasing? decreasing
The function f and it's derivitive f ' have many similarities.
When f ' (x)>0, than f is increasing.
When f ' (x)<0,>
Therefore f is increasing at the red line and decreasing at the purple line.

b)Where is f concave up? concave down?
When f ' (x) is increasing, than f is concave up.
When f ' (x) is decreasing, than f is concave down.

c)f(1)=0 is f(1) positive or negative? Explain.

2)Starting at time t=0 an object moves along the x-axis. The position x at time t is give by:
x(t)=t4-2t2-6t
a)Complete the table
The derivitive of position is velocity.
The derivitive of velovity is acceleration.
If you understand this it will be more clear into how to solve this. Remember derivitive means slope of the tangent line.


Things to keep in mind: When velocity and acceleration are opposite signs, speed is slowing down. When velocity and acceleration are the same signs, speed is speeding up.

Road Runner Example: When the coyote winds up with a big rubberband to try and catch the road runner.
Velocity is negative.
Acceleration is positive.
speed is slowing down.

There are many ways in solving this equation when using your calculator, I will name 3 of them:
#1) Using the 2nd DRAW Tangent(
#2)Y1=x^4-2x2-6x
Y2=nDeriv(Y1,x,x)
---------> the derivitive of velocity
Y3=nDeriv(Y2,x,x) ---------> the derivitive of acceleration

#3) Using the 2nd CALC dy/dx

b)At time t=1 is the objects speed increasing or decreasing? Explain.

Im still a bit confused about today's topics, so I'm sorry if things were not clear on my post. Any kind of help will be much appreciated. :)

HOMEWORK---> 2.5 exercise:Critical Numbers Relative Maximum and Minimum Points (odd numbers)

The next scribe shall be Suzanne :D

4 comments:

christian said...
This comment has been removed by the author.
christian said...

Yay! This is one of those relatively short, but informative and easy to understand posts. Kudos for you Crystal!

Just a couple of things. For the given graph of f'(x), I need clarification about the increasing and decreasing thing. To my understanding, wherever the y values are positive on the derivative function, that's where it is increasing on the parent function. In other words, there should be change of colours on the roots, not anywhere in between. I'D APPRECIATE CORRECTIONS IF I'M WRONG.

Manny said...

And now I'm confused too =S.

Mr.K. do you think we can go over just the graphs? Like.. from just looking at the parent function graph to be able to draw the derivitative graph, and vice-versa (derivative to parent function graph).

It takes me a bit of time to draw a derivative graph of the parent graph, but even then I'm still unsure. Sometimes I'm right, sometimes I'm wrong. When there's an equation, it's way easier to do because there's so many ways to tackle it (we did atleast seven in class). And if it's just me who's confused about it, I'll come see you during lunch. Okay, cool.

Mr. Kuropatwa said...

Tell you what ... tomorrow we'll look at graphs and graphs and graphs. ;-)