This is Critical
A critical point is when a derivative is this or that?
What is zero or undefined?
When testing for an absolute max or min value, we plug values into this equation.
What is f(x)?
This derivative tells us whether a function is increasing or decreasing.
The theorem that guarantees a point in a closed interval where the tangent line is parallel to the secant line connecting the endpoints of the interval.
What is the Mean Value Theorem?
This special day is coming soon on February 2.
What is Groundhog Day?
The critical points for f(x) =
(x^3)/3 -x^2 - 15x + 4
What is x = 5, -3?
A continuous function is guaranteed to have an absolute maximum and minimum value on a closed interval according to this theorem.
What is the Extreme Value Theorem?
This c-word is found from the 2nd derivative.
What is concavity?
(f(b) - f(a))/(b-a) = f'(c)
What is Mean Value Theorem?
There are this many states that start with the letter P.
What is one?
The critical points for f(x) =
x^3 - 12x^2
What is 0, 8?
The absolute minimum value over the interval [0, 3] of f(x) =
x^2 - 4x + 4
What is 0? (It occurs at x = 2.)
This point in the domain of a function is found when the 2nd derivative changes sign.
What is an inflection point?
The theorem that guarantees a point in an interval at which there will be a horizontal tangent line.
What is Rolle's Theorem?
The 13th number of the Fibonacci sequence. 0, 1, 1, 2, 3, ...
What is 144?
The critical points for f'(x) =
(x - 2)/(x + 4)
What is x = 2, -4?
The absolute maximum value over the interval [0, 3] of f(x) =
x^2 - 4x + 4
What is 4? (It occurs at x = 0.)
The interval where this function is increasing. f(x) =
x^2 - 6x + 9
What is [3, infinity)?
The number of "Derivative Tests" we learned.
What is 2?
The part of the cinnamon tree used to make cinnamon spice.
a.roots b.bark c.leaves d.berries
What is bark?
The critical points for f'(x) =
2/sqrt(x-9)
What is 9?
When finding the absolute max or min over a closed interval, we should test these values.
What are the endpoints and the critical points?
The x-coordinate of the inflection point of f(x) =
x^3 + 2x^2
What is
-2/3?
This derivative test is sometimes inconclusive?
What is the 2nd Derivative Test?
The king of this suit is the only one without a moustache.
What is hearts?