Letter of Advice to a Future Math Analysis Student

Dear Future Math Analysis Student,
                   If you want to pass the class, I advise you to look into any suggestions I may have for you. To be the most successful in this course, you need to be open to change, as Mrs. Kirch always says. This is because the classroom you are about to adapt to is called the flipped classroom, where we learn most of the material we would normally learn in class at home by watching videos. At first I didn't know if I was going to adapt well to this new style of learning but I wasn't going to fail the class. So I gave it a try and it was a big success. If you really want to be successful this year, do all your work right and completely. Take all your quizzes ahead of time and get your wsq chart signed off early. Also, always ask for help whenever you need it because that is what the flipped clasroom is designed to do. Mrs. Kirch is always going to be there whenever you need assistance. So don't worry.
                  To adjust to the flipped classroom in the best way possible, do everything on time and do all the work, because all the practice will surely benefit you when you take the test. Also, try to enjoy the class for a while because most of the time, you'll be working in groups in which you can collaborate in. Despite small distractions and little things here and there, my group definitely adjusted and had a great time doing so. Just be open to change because that's what's going to be your success. 
                 Unlike previous math classes you may have taken, this class does the opposite. Because we are able to learn at home and collaborate at school, your skills increase and you are able to apply what you know to reality better. You will create a blog, turn in online submissions and make tons of videos all so you can learn in the best way possible. You will use technology more in this class, increasing your skills in this field at the same time as learning new math. Overall, have a positive attitude when making the change and try to enjoy it a bit. I know I did. :)
               
                                                                    -Carlos
PS here's a video that can help clear up any confusion

Unit V Big Questions

The formula for the difference quotient comes from the derivative, that represents a formula which tells us the slope of the line that is tangent to any graph at any point. So, to get to the derivative, we must first evaluate the difference quotient. To do this, we find f(x+h), simplify f(x+h)-f(x), and divide the result from the previous step by h. Also, the slope of tangent line to a graph is the same as saying the derivative of a graph because the slope and tangent of a graph are on a and the same. To find the derivative, we evaluate the difference quotient as h approaches 0. Now, when we say the derivative, we say f prime of x (f'(x)) because this is a new equation. To find the slope of the tangent line to f(x) at a specific point, we find the derivative and plug in the x value of the point whose slope of the tangent line we are looking for. To find the equation of the tangent line at a specific point, we go even further and take the slope of the point given at the tangent line and use y=mx+b and find the whole equation with what we have. To find when the tangent line is horizontal, we find the first derivative of f(x), set it equal to zero to represent when the slope of f(x) is horizontal (0) and solve the resulting equation and get values of x where the tangent line would be horizontal.