Post #30

Hello everyone... again this week we took two more AP tests but this time they were made by someone different... so lets go over some concepts shall we:

First derivative test:

The problem will give you a function. They will ask you to look for max, min, or if the function is increasing or decreasing. You take the derivative of the function and set it equal to zero. Then you solve for the x values which are your critical points. Then you set the critical points up into intervals between negative infinity and infinity. Then you plug in numbers between those intervals into the first derivative and then solve.

Second derivative test:

Again, the problem will give you a function but this time they may want to know where the function is concave up, concave down, or where there is a point of inflection. You take the derivative of the function twice and set it equal to zero. You then solve for the critical points once again and set them up into intervals between negative infinity and infinity. Plug in numbers between those intervals into the second derivative and solve.

Tangent line:

The problem will give you a function and most of the time an x value. If no y value is given, you plug the x value into the original equation and solve for it. Then you take the derivative of the function and plug in the x value to find the slope. Once that is done, you set it up into point- slope form, y-y1=slope(x-x1).

Limit rules:

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

Things i do not understand:

I am still having problems with questions that give me a graph and i have to break the graph up into individual triangles and rectangles and then find the area.

I also have problems integrating trig functions.

I also have trouble when a problem mentions something is decaying or stuff like that. I just need to know where to start.

Have a great weekend :)