37th post

I can't believe this is the final blog before Wednesday's AP. Good luck to everyone and i hope you all do well. Here are some basic facts:

Limits:

If the degree on top is smaller than the degree on the bottom, the limit is zero.
If the degree on top is bigger than the degree on the bottom, the limit is infinity.
If the degree on top is the same as the degree on the bottom, you divide the coefficients to get the limit.

First derivative test:

You have to take the derivative of the function and set it equal to zero. Then solve for the critical values (x values). Set those values up into intervals between negative infinity and infinity. Plug in numbers between these intervals into the first derivative to see if there are max or mins or if the graph is increasing or decreasing.

Second derivative test:

You take the derivative of the function twice and set it equal to zero. Solve for the x values and set them up into intervals between negative infinity and infinity. Plug in numbers between those intervals into the second derivative to see where the graph is concave up, concave down, or where there is a point of inflection.

Tangent lines:

You will be given a function and a x value. If no y value is given, plug the x value into the original function and solve for y. Then take the derivative of the function and plug in the x value to get a slope. Then plug everything into point-slope form (y-y1=slope(x-x1)).

Normal lines:

You do the same thing as a tangent line except you take the negative reciprocal of the slope and plug in into point slope form.

Some things i still don't quite understand:
velocity, acceleration, and position problems
f inverse problems
related rates and angle of elevation
optimization

Have a great week everyone :)