Blog 9.

Alright, so this week was the start of the second nine weeks, and we started chapter three. Which doesn't seem like it's going to be too hard, although some of the rules are hard to remember. Anyways, we started off by learning what critical numbers were, which are max's and mins. So when something ask to find a critical number, you would be looking for the max or min. Now there are two theorems that you use, I don't have my binder with me so I'm not gonna go into detail to explain them because I don't want to give the wrong information. The two theorems are Rolle's theorem and Mean Value theorem. For each of these theorems your going to have to figure out if it's continuous and differentiable before continuing. Rolle's theorem deals with intervals, and it's to tell the max and min. Mean value theorem is dealing with slope. That's pretty much all I have to say about that since I don't have my binder. I'll explain section 3.3 since I know it. 3.3 is dealing with the first derivative test. The first derivative test has 3 steps to it: 1. Take derivative=0. 2. Solve for x. 3. Set up intervals, then plug back into derivative. (This will tell you whether the number is increasing or decreasing.)

Find the open intervals on which f(x)=x^3-3/2^x^2
1. 3x^2-3x=0
2. 3x(x-1)
x=0,1
3. (-infinity, 0) u (0,1) u(1,infinity)
4. f(-1)=+ f(1/2)=- f(2)=+
**Increasing (-infinity,0) u (1,infinity)
**Decreasing (0,1)
Now for something I don’t understand, I am still very confused with trig functions when it comes to problems like these.