Calculus, Limits and Continuity Can someone please answer/explain this question? Thank you.
1 answer:
9514 1404 393
Answer:
(A) -4 and -2
Step-by-step explanation:
The constant in the function tells you f(0) = 5.
You know that the positive leading coefficient means the value of f(x) will be negative for x-values smaller than some number. The offered answer choices indicate the value x = -4 is a lower bound on the value of c. So, -4 < c < 0, for sure.
To further refine the interval, you would need to know f(-2) and/or f(-1).
f(-2) = (-2)³ -2(-2) +5 = -8 +4 +5 = 1
Then -4 < c < -2.
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I find a graphing calculator to be very helpful locating zeros of polynomials.
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Answer: An integer added to an integer is an integer, this statement is always true. A polynomial subtracted from a polynomial is a polynomial, this statement is always true. A polynomial divided by a polynomial is a polynomial, this statement is sometimes true. A polynomial multiplied by a polynomial is a polynomial, this statement is always true.
Explanation:
1)
The closure property of integer states that the addition, subtraction and multiplication is integers is always an integer.
If , then a+b\in Z.
Therefore, an integer added to an integer is an integer, this statement is always true.
2)
A polynomial is in the form of,
Where are constant coefficient.
When we subtract the two polynomial then the resultant is also a polynomial form.
Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.
3)
If a polynomial divided by a polynomial then it may or may not be a polynomial.
If the degree of numerator polynomial is higher than the degree of denominator polynomial then it may be a polynomial.
For example:
Then , which a polynomial.
If the degree of numerator polynomial is less than the degree of denominator polynomial then it is a rational function.
For example:
Then , which a not a polynomial.
Therefore, a polynomial divided by a polynomial is a polynomial, this statement is sometimes true.
4)
As we know a polynomial is in the form of,
Where are constant coefficient.
When we multiply the two polynomial, the degree of the resultand function is addition of degree of both polyminals and the resultant is also a polynomial form.
Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.