Mins/Maxs
Second Derivative
Optimization
***missing graphs***
Graphs of f, f' and f"
Random
100
The definition of a critical point
What is a point where the derivative is zero or doesn't exist?
100
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 a point of inflection?
100
The difference of two numbers is 44. Find their minimum product.
What is -484?
100

***desmos graph*** 

How many points of inflection does this graph have?

What is 3?

100
If f' is increasing, then f" is..
What is positive?
200
What the first derivative test finds.
What are relative maximums and minimums?
200
When the second derivative is positive, the first derivative is______
What is increasing?
200
Find two positive numbers whose product is 196 but whose sum is minimum
What is x=14 and y=14?
200

***desmos graph***

If this is the graph of f', where is f concave up?

What is (-∞, -3) (-1, 2) and (4, ∞)?

200
If f is concave down, then f' is....
What is decreasing?
300
Find the relative min of (x+2)^2 - 4
What is (-2,-4)?
300
Determine the interval(s) where y=x^3+3x^2+6 is concave up.
What is (-1, infinity)?
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

***desmos graph***

If this is the graph of f', then where does f have relative maximum?

What is at x=-2, and x = 3?

300
Find the c value guaranteed by the Mean Value Theorem for f(x) = x^2-3x on the interval [1, 4].
What is x=2.5?
400
Why is (0 , 0) not an Extrema of the function f(x) = x^4 - 4x^3.
f' does not change sign at 0.
400
Find the equation of the tangent line to the graph of y=x^3+6x^2 at its Point of Inflection.
What is y=-12(x+2)+16?
400
A manufacturer needs to make a cylindrical can that will hold 1500 cm^3 of liquid. Determine the dimensions of the can that will minimize the amount of material used in its construction.
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

***missing graph***

If this is the graph of f', where are the Points of Inflection of f?

What is x=-3 x=-1, x=2, x=4?

400
Let f(x) be a polynomial function such that f(3)=5, f'(3)=0, and f "(3)=-2. The point (3, 5) is a ________________________ of the graph of f. (Be specific.)
What is a relative maximum?
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