SOUTHERN NEW HAMPSHIRE UNIVERSITY - 7-3 CALCULUS I:
SINGLE-VARIABLE CALCULUS (MAT225) PROJECT TWO - GAME
TESTING ROUND TWO 2025
, [PRINT]
Question1: Score 1/1
Crossing the Room
You receive a response from your home planet with details on
how to escape the planet. You are directed to connect your
computer to the alien computer as a means to gather
information. You are told that there is a spacecraft that can get
you home, but it is guarded by several gates and traps. Your
computer has informed you that the raw ingredients for fuel are
available, but the amount of fuel in the ship is unknown. The
first step is to travel across a room that includes hidden traps in
the floor. There are safe places where you must stop in order to
make it across the room safely. The location of these safe
spaces will be translated into mathematics, which you can
solve, and then program into your computer. Your computer will
then detail precisely where you can stop in the room. Your
computer translates the following:
Find the open intervals on which the function
f (x) = x + 4√1 − x is increasing or decreasing. The safe
points will be calculated from these intervals. If the function is
never increasing or decreasing, provide an input of NA to your
computer.
Increasing
Interval:
Your response Correct response
(-infinity, -3) (−∞, −3)
Auto graded Grade: 1/1.0
Decreasing
Interval:
Your response Correct response
(-3, 1) (−3, 1)
Auto graded Grade: 1/1.0
, Explain, in your own words and with your own work, how
you arrived at this result. Be sure to explain using calculus
concepts to best support the work of the game design
team.
To find the intervals where f (x) = x + 4√1 − x is increasing and decreasing, we first
should find the domain of our function.
The section under the square root cannot be negative.
Therefore, 1 − x ≥0 → 1≥x
So our domain of f (x) is (−∞, 1]
Now to find the derivative with respect to x
4(−1)
f ′ (x) = 1 +
2√1−x
f ′ (x) = 1 − 2
√1−x
With our derivative, we use the equation to solve for f'(x) > 0 for increasing interval
and then take its intersection with the domain.
1− 2 > 0 → x < −3
√1−x
We need to take the intersection with the domain for increasing intervals.
We get, x ∈ (−∞, −3) ∩ (−∞, 1)
Therefore, our increasing interval is (−∞, −3)
Now we will do the same for our decreasing interval, except f'(x) < 0 now
1− 2 < 0 → x > −3
√1−x
We need to take the intersection with the domain for decreasing intervals.
We get, x ∈ (−3, ∞) ∩ (−∞, 1)
Therefore, our decreasing interval is (−3, 1)
Ungraded Grade: 0/0.0
Total grade: 1.0×1/2 + 1.0×1/2 + 0.0×0/2 = 50% + 50% + 0%
Question2: Score 1/1
SINGLE-VARIABLE CALCULUS (MAT225) PROJECT TWO - GAME
TESTING ROUND TWO 2025
, [PRINT]
Question1: Score 1/1
Crossing the Room
You receive a response from your home planet with details on
how to escape the planet. You are directed to connect your
computer to the alien computer as a means to gather
information. You are told that there is a spacecraft that can get
you home, but it is guarded by several gates and traps. Your
computer has informed you that the raw ingredients for fuel are
available, but the amount of fuel in the ship is unknown. The
first step is to travel across a room that includes hidden traps in
the floor. There are safe places where you must stop in order to
make it across the room safely. The location of these safe
spaces will be translated into mathematics, which you can
solve, and then program into your computer. Your computer will
then detail precisely where you can stop in the room. Your
computer translates the following:
Find the open intervals on which the function
f (x) = x + 4√1 − x is increasing or decreasing. The safe
points will be calculated from these intervals. If the function is
never increasing or decreasing, provide an input of NA to your
computer.
Increasing
Interval:
Your response Correct response
(-infinity, -3) (−∞, −3)
Auto graded Grade: 1/1.0
Decreasing
Interval:
Your response Correct response
(-3, 1) (−3, 1)
Auto graded Grade: 1/1.0
, Explain, in your own words and with your own work, how
you arrived at this result. Be sure to explain using calculus
concepts to best support the work of the game design
team.
To find the intervals where f (x) = x + 4√1 − x is increasing and decreasing, we first
should find the domain of our function.
The section under the square root cannot be negative.
Therefore, 1 − x ≥0 → 1≥x
So our domain of f (x) is (−∞, 1]
Now to find the derivative with respect to x
4(−1)
f ′ (x) = 1 +
2√1−x
f ′ (x) = 1 − 2
√1−x
With our derivative, we use the equation to solve for f'(x) > 0 for increasing interval
and then take its intersection with the domain.
1− 2 > 0 → x < −3
√1−x
We need to take the intersection with the domain for increasing intervals.
We get, x ∈ (−∞, −3) ∩ (−∞, 1)
Therefore, our increasing interval is (−∞, −3)
Now we will do the same for our decreasing interval, except f'(x) < 0 now
1− 2 < 0 → x > −3
√1−x
We need to take the intersection with the domain for decreasing intervals.
We get, x ∈ (−3, ∞) ∩ (−∞, 1)
Therefore, our decreasing interval is (−3, 1)
Ungraded Grade: 0/0.0
Total grade: 1.0×1/2 + 1.0×1/2 + 0.0×0/2 = 50% + 50% + 0%
Question2: Score 1/1
