Academic Detention Blog #3

So once again i am just going to go back to the basics becuse i feel that if i take the time to explain it that it will be a good review for the exam on tuesday which will probably kick my butt.

so average speed and instantanious speed here we go.

lets talk about the differences between the two topics because i often get the mixed up. the difference between average speed and instantaneous speed is that instantaneous speed refers to the speed only during that instant. Average speed, on the other hand, refers to the speed during or over a particulare period of time.

EXAMPLE PROBLEM:

a bag of flower is dropped off of a roof on to the car, what is the average speed during the first two seconds of falling. Given: y=16t^2 to describe the fall.
x=(0,2)- this represents the first two secons.
to find your y's you would plug the first x and then the second x into the given equation.
f(0)=0 and f(2)=16(4)=64
after completin those steps, you plug in to your slope formula.
(y2-y1)/(x2-x1)=(64-0)/(2-0)= 32
the average speed of this particular problem would be 32 m/s.

Optimization- a process that stretches an equation. first you determine all quantities of the equation, then you write a new equation, reduce it and determine the domain of the equation, then from there you determine the max's and min's of the equation. optimization is usefull when dealing with area and volume.

Mean value thereom - somewhat like rolles. says that if a function is continous and differentiable then, f^(c) = f(b)-f(a)/b-a. saying that when its continous and differentiable on the interval then the value c exist on that interval.