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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Which of the following shaded intervals is the graph of the inequality
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10 Mar 2022, 12:20
10 Mar 2022, 12:20
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42% (02:36) correct
57% (02:38) wrong based on 26 sessions
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Which of the following shaded intervals is the graph of the inequality \(-x^3 - 10x^2 + 24x ≤ 0\)?
Re: Which of the following shaded intervals is the graph of the inequality
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10 Mar 2022, 12:24
10 Mar 2022, 12:24
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Expert Reply
Great question
Which of the following shaded intervals is the graph of the inequality
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07 Sep 2022, 12:35
07 Sep 2022, 12:35
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\(-x^3 - 10x^2 + 24x ≤ 0\)
First, get rid of the negative in front of \(x^3\) by multiplying both sides of inequality by -1 and flipping the sign. Then, you will want to factor the inequality:
\(x^3 + 10x^2 - 24x ≥ 0\)
\(x(x^2 + 10x - 24) ≥ 0\)
\(x(x+12)(x-2) ≥ 0\)
The roots of the inequality:
\(x = 0, x = -12, x = 2\)
Plug in numbers to see which intervals are positive.
When x = 3, we get the following: (3)(3+12)(3-2) = (3)(15)(1) > 0.
When x = -1, we get the following: (-1)(-1+12)(-1-2) = (-1)(11)(-3) > 0.
We are done testing numbers and based on the answer choices, C has the correct shaded intervals.
First, get rid of the negative in front of \(x^3\) by multiplying both sides of inequality by -1 and flipping the sign. Then, you will want to factor the inequality:
\(x^3 + 10x^2 - 24x ≥ 0\)
\(x(x^2 + 10x - 24) ≥ 0\)
\(x(x+12)(x-2) ≥ 0\)
The roots of the inequality:
\(x = 0, x = -12, x = 2\)
Plug in numbers to see which intervals are positive.
When x = 3, we get the following: (3)(3+12)(3-2) = (3)(15)(1) > 0.
When x = -1, we get the following: (-1)(-1+12)(-1-2) = (-1)(11)(-3) > 0.
We are done testing numbers and based on the answer choices, C has the correct shaded intervals.
