Post 3

So far this week we've only really learned two new things. We learned how to take the first and second derivative from a graph, and we also learned how to find a first derivative by using the first derivative test.

Along with learning the first and second derivatives, we've learned the vocabulary associated with the graphs. We learned that the words increasing, decreasing, and minimum and maximum are related to the origional graph; positive slope, negative slope, and horizontal tangent are related to the first derivative; concave up and concave down are related to the second derivative. We learned that when there's a positive slope and the graph concaves up, the derivative will be above the axis, that if a slope is negative and it concaves down the derivative will be below the axis, and if a derivative has a zero, it will form a horizontal tangent and a point of inflection.

To find the first derivative, there are steps to follow:
1. take a derivative
2. set it equal to zero
3. solve for x giving you either max, min, horizontal tangents, extrema, or critical points
4. set up intervals using step 3
5. plug in first derivative
6. to find an absolute max/min, plug values from step 5 into the origional function and check end points
7. remember to check for all points of continuity

If the question would ask you either where the graph is increasing or decreasing, or where the horizontal tangent or min and max are, you would stop at step number 3 and be finished with the problem. If the problem would as you something like "Find the relative max and min" you would bo on to steps 4 through 7 setting up your intervals and plugging values into the first derivative and the origional function.

The only real problem I had this week was looking at the graphs and trying to decide how to get the first and second derivatives out of them. I just get lost from the beginning looking at the graphs. I think if I have more practice on the graphs I'll do fine.