20th post

Goodbye 2009... hello 2010.. i hope everyone's holidays were good. Let's start off with some of the basics.

To remind anyone who does not know how to take a derivative here are some examples.

Let's say you have the function 4x^2 +5x+6. To take the derivative, you would multiply the 4 and the 2 and then subtract the 2 by 1. For the 5x, you would simply get rid of the x, and the 6 would become zero. So the final answer would be 8x +5.

Some other things to remember is the first and second derivative test. When using the first derivative test, you look for max and mins, and increasing and decreasing. To use the first derivative test, you take the derivative of the original function and solve for x. The x values are called critival values. You then plug these critical values into intervals between negative infinity and infinity. To find out whether your function is increasing or decreasing, you plug in numbers between your intervals into the derivative. If the number is positive it is increasing, if then number is negative then it is decreasing.

Another thing to remember is the second derivative test. It is basically the same thing as the first derivative test; however, you are taking the derivative twice and you are looking for different things such as change in concavity and points of inflection. You take the derivative of the original function twice and solve for x to get the critical values and set them up into intervals. You then plug in numbers between the intervals to see whether the function is concave up or concave down. If the number is positive it is concave up, if the number is negative it is concave down. Where there is a difference in concavity, there is a point of inflection.

Some of the things i am still having trouble with is optimization. I just cannot get a grasp on the concept. See all of you at school tomorrow!