Features Of Polynomials
What do you know about the features of polynomials are? Would you be able to achieve a high score on this quiz? Polynomial features are those features created by raising existing features to an exponent. They are an expression containing variables and coefficients. These include addition, multiplication, subtraction, and non-negative integer exponentiation of variables in mathematics. This quiz will help you appreciate more about the features of polynomials.
- 1.
For a polynomial P(x) defined on an interval [a,b], where do you need to check for minima and maxima?
- A.
Wherever P(x) = 0
- B.
Wherever P'(x) = 0
- C.
Wherever P''(x) = 0
- D.
At x = a and x = b
Correct Answer(s)
B. Wherever P'(x) = 0
D. At x = a and x = b -
- 2.
Statement: An absolute (global) maximum is also a relative (local) maximum.
- A.
True
- B.
False
Correct Answer
A. True -
- 3.
Statement: Relative (local) extremes cannot occur at endpoints unless the slope of the tangent line at the endpoint is zero.
- A.
True
- B.
False
Correct Answer
B. False -
- 4.
Statement: A point of inflection is found at any location where the second derivative of a function is zero.
- A.
True
- B.
False
Correct Answer
B. False -
- 5.
Statement: At a location where the first derivative of a function is zero, the function may have a local minimum, a local maximum, or a point of inflection.
- A.
True
- B.
False
Correct Answer
A. True -
- 6.
Statement: The slope of the tangent line at a point of inflection is always zero.
- A.
True
- B.
False
Correct Answer
B. False -
- 7.
Consider the polynomial f(x) and the sign line shown for its derivative f'(x). Which statement best describes the relative extrema of f?
- A.
The function f has relative minima at –2 and 5/2, and a relative maximum at 0
- B.
The function f has a relative minimum at 0 and a relative maximum at 5/2
- C.
The function f only has one relative extreme: a maximum at –2
- D.
The function f has a relative maximum at 0 and a relative minimm at 5/2
Correct Answer
D. The function f has a relative maximum at 0 and a relative minimm at 5/2 -
- 8.
Consider the polynomial f(x) and the sign line shown for its derivative f'(x). Which statement about increasing vs. decreasing is true?
- A.
The function f is increasing on the interval [–1,1]
- B.
The function f is decreasing on the inverval [–1,1]
- C.
The function f is decreasing on the interval [0,5/2]
- D.
The function f is overall an increasing function
Correct Answer
C. The function f is decreasing on the interval [0,5/2] -
- 9.
Consider the polynomial f(x) and the sign line shown for its derivative f'(x). Which statement about inflection points of f is definitely true?
- A.
The function f does not have any inflection points
- B.
The function f has an inflection point at –2 and possible inflection points at 0 and/or 5/2
- C.
The function f has an inflection point at –2 and potentially other inflection points, but NOT at 0 or 5/2
- D.
The function f has exactly four inflection points
Correct Answer
C. The function f has an inflection point at –2 and potentially other inflection points, but NOT at 0 or 5/2 -
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Current Version
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Mar 18, 2022Quiz Edited by
ProProfs Editorial Team -
Oct 05, 2020Quiz Created by
I-heng_mccomb
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