Assignment #6

The second derivative test is used to determine whether or not at specific x values in a differentiable function can have relative extrema. This is determined by plugging in the critical numbers of the equation, making the equation positive or negative. If it is negative there it is concave down and has a relative max, if it is positive then it is concave up creating a relative min. To do all this you must use the first derivative, which finds the critical numbers allowing you to determine the concavity, relative max and relative min.

Assignment #5

Due to the use of a differentiable function, f(3)=30 and f(5)=30 therefore f(3)=f(5). This also means that there is a different value for x between 3 and 5, which is f(4)=25. According to Rolle's Theorem, there must be at least one point between 3 and 5 where the rate is equal to 0

Assignment #4

http://apcentral.collegeboard.com/apc/public/repository/ap07_calculus_ab_frq.pdf

Question five deals with related rates because a quantity is changing, in this case the volume of the balloon, in relation to the other quantities in the problem which would be the balloons radius, all in respect to time.

Assignment #3

We can use the chain rule in order to solve the problem f(x)=(3x+1)^2. The derivative turns out to be f '(x)=6(3x+1). In order to use the chain rule you must multiply the function by two and subtract one from the exponent. In the beginning it becomes 2(3x+1), then you must determine the derivative of whats inside, which is 3. You must then multiply the function 2(3x+1) by 3 becoming 6(3x+1).

Assignment #2

The Intermediate value theorem explains how a function is continuous over a given interval. If a function is continuous over a given interval then there is a value of that function. Determining if it is continuous or not allows us to find the possible limits within the problem. The Intermediate value theorem is a existence theorem because it shows the value between two points whether it is continuous or not and whether it has to pass through a point to go to another.

Assignment #1

I joined AP Calculus BC because I wish to pursue a career in math. I also wanted to challenge myself and have a smaller class. I wish to get a better understanding of Calculus and taking a course that will challenge me will help me accomplish my goals.