Before i start talking about Calculus i hope everyone had a great week off! To start this blog off, i'll go over the things i definitely know:
First derivative test:
In the problem, they will give you a function, and they will ask if it is increasing, decreasing, a max or a min. To do this you have to use the first derivative test. you take the derivative of the original function and solve for your x values (critical points). Then you set those points up into intervals and then plug in numbers between those intervals into the derivative. if the answer is positive it is increasing, if it is negative it is decreasing.
Second derivative test:
it will be set up like the first derivative test except they will ask if the function is concave up or concave down. They may also ask where there is a point of inflection. To do this you must use the second derivative test. You take the derivative of the function twice and solve for your critical values and set them up into intervals. You then plug numbers between those intervals into your second derivative to see where there is a change in concavity. If the answer is positive it is concave up; if the answer is negative it is concave down; where there is a change in concavity there is a point of inflection.
Limit Rules:
1. If the degree on top is smaller than the degree on the botton, then the limit is zero.
2. If the degree on top is bigger than the degree on the bottom, then the limit is infinity.
3. If the degree on top is the same as the degree on the bottom, you divide the coefficients to get the limit.
If they give you a limit and ask what is the limit as a h goes to a number, you must take the derivative of the number behind what is in the parenthesis on top, then substitute the number in for any x value.
Some things i still do not understand:
the particle problems
Angle of elevation
related rates
See everyone on Monday :)
Subscribe to:
Post Comments (Atom)
This comment has been removed by the author.
ReplyDeleteRELATED RATES:
ReplyDelete1. identify all variables and equations
2. identify what you are looking for
3. sketch and label
4. write an equations involving your variables (you can only have one unknown so a secondary equation may be given)
5. take the derivative (with respect to time)
6. substitute in derivative and solve
for related rates u first identify all variables and equations thenidentify what you are looking for then sketch and label then write an equations involving your variables (you can only have one unknown so a secondary equation may be given)then take the derivative (with respect to time)then substitute in derivative and solve
ReplyDeletefor your particle problems remember its
ReplyDeleteposition
velocity
acceleration
When going from top to the bottom take the derivative so to find velocity take the first derivative and take the second derivative to find acceleration
When going from the bottom to top integrate
hope this helps
particle problems use lots of key words.
ReplyDeletethey have to be listed in the right order, or the trick will not work.
it goes
POSITION
VELOCITY
ACCELERATION
i remember it as PVA, kinda like PDA. haha i know thats weird but whatever!
when moving DOWN, take the derivative.
so if given position and asked for velocity, your moving down the list.
when moving UP, take the integral.