Post #32

This week in calculus we went over some of the concepts we did not know very well. Let's go over some simple concepts.

Product Rule:

When taking the derivative, sometimes you have to use the product rule. You take the derivative of the first and then leave the second as is, then add a plus sign and leave the first as is and take the derivative of the second.

Chain Rule:

For a chain rule, you will have a function raised to a power. For example, lets say you have (2x)^3, You have to bring the 3 out in front and then take the derivative of the inside. So you end up with 6(2x)^2.

First derivative test:

The problem will give u a function and you have to take the derivative of that function and solve for the x values. Then you plug those x values into intervals between negative infinity and infinity. Then plug in numbers between those intervals into the derivative to find if the function is a max, min, increasing or decreasing.

Second derivative test:

You take the derivative of the function twice and solve for the x values once more. Set those values up into intervals between negative infinity and infinity. Plug in a number between these intervals into the second derivative to see if it is concave up, concave down, or a point of inflection.

Tangent line:

if no y value is given, plug the x value into the original function to find the y value. Then take the derivative of the function and plug in the x value to find the slope. Once this is done, plug everything into point-slope form y-y1=slope(x-x1).

Things i still have trouble with:

-area problems where u have to find the bounds
- When they give you a graph of acceleration and you have to find where the initial position is
-Problems where they want you to find the increase in value between years (2005-2007).

Have a great weekend :)