
Maximizing Volume and Revenue: Cubic Function Challenges
Authored by Anthony Clark
English, Mathematics
9th Grade
CCSS covered

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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A box with a square base and height is to be constructed. If the volume of the box is given by the function V(x) = x^2(10 - x), where x is the length of the side of the base, what is the maximum volume of the box?
120.5
148.14814814814815
160.75
135.0
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The revenue R from selling x units of a product is modeled by the function R(x) = -2x^3 + 30x^2 + 50. How many units should be sold to maximize revenue?
5.75
2.50
3.16
4.00
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A water tank has a cubic shape, and its volume is given by V(s) = s^3, where s is the length of a side. If the tank is filled to a height of 5 meters, what is the volume of water in the tank?
100 cubic meters
75 cubic meters
150 cubic meters
125 cubic meters
Tags
CCSS.8.EE.A.2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The height of a projectile launched into the air is modeled by the function h(t) = -4.9t^3 + 20t^2 + 5, where t is time in seconds. What is the maximum height reached by the projectile?
h(0) = 5
h(2) = 25
h(1.054) = 15.5
h(1.5) = 18
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A farmer wants to create a rectangular field with a cubic fence. The volume of the fence is given by V(x) = 3x^3 + 12x^2 + 9x. What is the critical point that maximizes the volume of the fence?
0
2
-3
-1.5
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The profit P from producing x items is given by P(x) = -x^3 + 15x^2 - 24x. What is the maximum profit that can be achieved?
36.08
48.50
24.00
30.75
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A car's speed is modeled by the function S(t) = 2t^3 - 15t^2 + 36t, where t is time in seconds. At what time does the car reach its maximum speed?
3 seconds
5 seconds
1 second
2 seconds
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