Initial Value problems:
When you are given a rate of change and you want to find a new value at a new time or something.
Usually if you KNOW velocity, but you want a position.
Sometimes they will give you the derivative of a rate, but you WON’T need it, the rate you get is all that you need.
REMEMBER to read if it is a rate or a position function.
If they give you an interval STICK WITH IT, do not put in 0 if the problem only wants 20 to 25.
The average height of a function on an interval:
The Area/Integral of the function divided by the length of the interval
Rates In and Out:
Is the level of liquid RISING or FALLING at a certain time:
Simply evaluate each function at the given time and take the difference.
How much liquid do we have at a given point in time:
You will get the initial value in the beginning of the problem, and time is “b”