
Concavity and Function Behavior Quiz
Quiz
•
Mathematics
•
12th Grade
•
Practice Problem
•
Medium
Standards-aligned
Eddy Mkwambe
Used 1+ times
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10 questions
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1.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
Determine the concavity of the function f(x) = 3x^2 - 6x + 2.
The function f(x) = 3x^2 - 6x + 2 has no concavity.
The function f(x) = 3x^2 - 6x + 2 is concave down.
The function f(x) = 3x^2 - 6x + 2 is linear.
The function f(x) = 3x^2 - 6x + 2 is concave up.
2.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
Find the concavity of the function g(x) = x^3 - 6x^2 + 9x - 4.
The concavity of the function g(x) = x^3 - 6x^2 + 9x - 4 is downward (or concave down).
The concavity of the function g(x) = x^3 - 6x^2 + 9x - 4 is linear.
The concavity of the function g(x) = x^3 - 6x^2 + 9x - 4 is upward (or concave up).
The concavity of the function g(x) = x^3 - 6x^2 + 9x - 4 is undefined.
Tags
CCSS.HSF.IF.A.2
3.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
Analyse the behavior of the function h(x) = 4x^3 - 12x^2 + 8x.
The function h(x) = 4x^3 - 12x^2 + 8x has no specific behavior
The function h(x) = 4x^3 - 12x^2 + 8x is always decreasing
The function h(x) = 4x^3 - 12x^2 + 8x is always increasing
The function h(x) = 4x^3 - 12x^2 + 8x exhibits behavior of increasing from negative infinity to 1, then decreasing from 1 to 2, and increasing from 2 to positive infinity.
4.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
Examine the behavior of the function k(x) = -2x^3 + 6x^2 - 4x.
The function k(x) = -2x^3 + 6x^2 - 4x is a linear function, so it will have a constant end behavior for all x values.
The function k(x) = -2x^3 + 6x^2 - 4x is an exponential function, so it will have end behavior that oscillates as x approaches infinity.
The function k(x) = -2x^3 + 6x^2 - 4x is a quadratic function, so it will have end behavior that approaches negative infinity as x approaches positive infinity.
The function k(x) = -2x^3 + 6x^2 - 4x is a cubic function, so it will have end behavior that approaches negative infinity as x approaches negative infinity, and end behavior that approaches positive infinity as x approaches positive infinity.
5.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
Identify the intervals of increasing and decreasing for the function f(x) = x^4 - 4x^3 + 6x^2 - 4x + 1.
The intervals of increasing are (-∞, 1) and the intervals of decreasing are (1, ∞)
The intervals of increasing are (-∞, 0) and the intervals of decreasing are (0, ∞)
The intervals of increasing are (1, ∞) and the intervals of decreasing are (-∞, 1)
The intervals of increasing are (-∞, 2) and the intervals of decreasing are (2, ∞)
6.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
Determine the intervals of increasing and decreasing for the function g(x) = -2x^4 + 8x^3 - 12x^2 + 8x.
The function g(x) is increasing on the intervals (-∞, 2) and (3, ∞), and decreasing on the interval (2, 3)
The function g(x) is increasing on the intervals (-∞, 2) and (3, ∞), and decreasing on the interval (2, 3)
The function g(x) is increasing on the intervals (-∞, 0) and (1, ∞), and decreasing on the interval (0, 1)
The function g(x) is increasing on the intervals (-∞, 1) and (2, ∞), and decreasing on the interval (1, 2).
7.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
Apply the first derivative test to find the local extrema of the function f(x) = 2x^3 - 6x^2 + 4x - 1.
f(x) has local maxima at x = 2 and local minima at x = 1
f(x) has local maxima at x = 1 and local minima at x = 2
f(x) has local maxima at x = -1 and local minima at x = 2
f(x) has local maxima at x = 0 and local minima at x = 3
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