Show:
Mins/Maxs
Concavity
Optimization
Asymptote
Bonus
100
The definition of a critical point
What is a zero of the derivative or a place where it doesn't exist?
100
The test that determines concavity
What is the second derivative test?
100
The Primary Equation
What is the equation that you want to maximize or minimize?
100
Take the limit of the function as x approaches infinity. (What will this find in reference to the graph of the function?)
What do you do to a function to find if the function contains horizontal asymptotes?
100
The year Mr. Smucker graduated from high school
what is 2010
200
The purpose of the first derivative test
What is finding the slope of the function before and after a critical point (i.e. determining if the critical point is a relative min or max)
200
When the second derivative is positive/negative
When is the function concave up/down?
200
xy=192, from the problem: find two positive numbers whose product is 192 but whose sum is minimum
What is the secondary equation
200
The vertical and horizontal asymptotes of (3x)/(x^2-4)
What is x=2,-2 and y=0?
200
Mr. Smucker's favorite TV show
What is Scrubs
300
the relative min of (x+2)^2 - 4
What is (-2,-4)
300
f "(c) > 0 where c is a critical number.
What is the value of the second derivative of a function on an interval where the original function, f(x), is concave up?
300
We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field and so won’t need any fencing. Determine the dimensions of the field that will enclose the largest area.
The dimensions of the field that will give the largest area, subject to the fact that we used exactly 500 ft of fencing material, are 250 x 125.
300
Direct substitution of a value, c, into the original function indicates a vertical asymptote exists if...
What is f(c) = constant / 0
300
The two cites has Mr. Smucker lived in
What is Canby and Seattle
400
Why is (0 , 0) not an Extrema of the function f(x) = x^4 - 4x^3.
It is the point of inflection, not a minimum or maximum.
400
The point on the graph of a function of which the concavity changes from concave up to concave down or concave down to concave up.
What is the point of inflection?
400
A manufacturer needs to make a cylindrical can that will hold 1.5 liters of liquid. Determine the dimensions of the can that will minimize the amount of material used in its construction. (Hint: Use the fact that 1 Liter = 1000 cubic centimeters. Thus 1.5 liters is equivalent to 1500 cubic cm.)
Therefore if the manufacturer makes the can with a radius of 6.2035 cm and a height of 12.4070 cm the least amount of material will be used to make the can.
400
A discontinuity in the original function that is not a vertical asymptote. The result of direct substitution into a rational function.
What is 0/0.
400
The man who said, "To give anything less than your best is to sacrifice the gift."
Who is Steve Prefontaine
500
In the movie Zoolander name two actors that were actually family
Who is Zoolander and Maury (father and son) Zoolander and Matilda (Husband and wife)