Vocab
Another word for rate of change is _______
slope
A word for the rate of change of the rate of change is ______________
concavity
The function P models the population of rabbits on a farm: P(t) = 200t/(1 + 5t), where t is measured in months since the start of the year and t>=0. What does the rabbit population approach after a large number of months?
40
If a slope is negative and increasing over a given interval, we can describe it as ____________
Concave Up
Describe the behavior of the following function at each of its zeros:
f(x) = (x + 6)(x - 2)(x - 2)
At x = 2, the graph of f touches the x-axis and "bounces" off (forms a parabola)
If a slope is positive and decreasing over a given interval, we can describe it as ______________
Concave Down
Explain how the leading coefficient of a rational function, such as
R(x) = (2x3 - 6x2 + 7) / (4x2 - 5x -2)
Effects the function's behavior at infinity
If the numerator and denominator have the same highest power, the limit approaches the ratio of their coefficients.
If the numerator's highest power is greater than the denominator's, the function will approach infinity.
If the denominator's highest power is bigger, the function will approach 0.
A teacher has 2 Arabic books, 3 German books, and 4 Spanish books. How many ways can he arrange them on a book shelf if the Arabic books must stay together and the Spanish books must stay together?
5!4!2! = 5,760 ways
The point where the concavity of a function changes is called a ____________.
Point of Inflection
If 3 vertices inside a regular octagon are randomly connected to form a triangle, what is the probability that at least one of the triangle sides is the same as one of the octagon sides?
Write your answer as a fraction.
(8 + 8*4) / (8 Choose 3)
= 40/56 = 5/7