Calculating Critical Points
What is the critical value for the equation y = x2?
x=0
Is a critical point where the first derivative is positive to the right and negative to the left a relative maximum or a relative minimum
Relative minimum
Is the function f(x) = 2x2 - 3 increasing or decreasing on the interval [negative infinity, 0]?
Show work for first derivative test
Decreasing
The shortest day of the year
What is the Winter Solstice
The plastic piece at the end of a shoelace
what is an aglet
What are the rules to find a critical point?
When f'(x) = 0 and when f(a) is defined and f'(a) = undefined
Is the critical point of y = 1/6 x2 + 2x a max or min?
Min
Name the intervals on which the function
f(x) = 2x3-9x2-108x+2 is increasing.
f(x) is increasing on the intervals:
negative infinity < x < -3 and 6 < x < infinity
Only bird that can fly backwards
What is a hummingbird
Water runs into a conical tank at the rate of 9 cubic feet per minute. The tank stands pointed downward and has a height of 10 feet and a base radius of 5 feet. How fast is the water level rising when the water is 6 feet deep?
1/π feet per minute
What is the critical point for any linear function given y = mx + b?
There are no critical points
What is the absolute min for the function
f(x) = x4+2x3-2x2+1 on the interval [-2,1]
(-2,-7)
Is the function f(x) = 4x4 + 3x3 - 12x2 + 6 increasing or decreasing as it approaches infinity?
increasing
The host of Jeopardy
Who is Alex Trebek
Actor who played Neo in The Matrix
Who is Keanu Reeves.
Name the Critical Points for the function f(x) = 3x4−4x3−12x2+3?
(0,3),(-1,-2),(2,-29)
Is the critical point of y=x3-1 a max or min?
Neither it is an inflection point.
Where is the function f(x) = 4e-x^2 increasing and decreasing?
increasing: x < 0
decreasing: x > 0
Youngest self made billionaire
Who is Kylie Jenner
Winning team of Super Bowl LIII
Who is the New England Patriots
What are the critical values for the equation f(x) = sinxcosx on the interval [0,2π]?
x = (π/4,3π/4,5π/4,7π/4)
What is the absolute maximum and absolute minimum of the function y=cos(2x)−x on the interval [0,2π]?
absolute min at x=7π/12,
absolute max at x=−π/12
Where is the function f(x) = |x2-9| increasing and decreasing?
increasing: -3 < x < 0, x > 3
decreasing: x < -3, 0 < x < 3
First toy to be advertised on television
(HINT: it involves a vegetable)
What is Mr. Potato Head
According to the FDA, this is the only fish that produces real caviar.
What is the sturgeon.