graph h(x)=x^4-3x^2+x. identity the x intercepts and the points where the local maximum and local minimum occur. determine the intervals for which the function is increasing or decreasing.Round to the nearest hundredth if necessary
Answers
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The x-intercept are x = 0, x = -1.9, x = 0.35, and x = 1.5.
The local minimum is 1.
The function is increasing at the interval (-1.5, 0.5) and (1, ∞).
The function is decreasing at the interval (∞, -1) and (0, 1.5).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
h(x) = [tex]x^4[/tex] - 3x² + x
The x-intercept is when h(x) = 0.
0 = [tex]x^4[/tex] - 3x² + x
From the graph, we see that,
The x-intercept are at x = 0, x = -1.9, x = 0.35, and x = 1.5
Now,
h(x) = [tex]x^4[/tex] - 3x² + x
h'(x) = 4x³ - 6x
h''(x) = 12x² - 6 (positive)
So,
h(x) has a minimum value.
h'(x) = 0
4x³ - 6x = 0
4x³ = 6x
4x² = 6
x² = 6/4
x² = 3/2
x² = 1.5
x = ±√1.5
x = ±1.22
The minimum values are:
h(1.22) = [tex]x^4[/tex] - 3x² + x = -1
h(-1.22) = [tex]x^4[/tex] - 3x² + x = 1
The local minimum is 1.
From the graph, we see that,
The function is increasing at the interval (-1.5, 0.5) and (1, ∞).
The function is decreasing at the interval (∞, -1) and (0, 1.5).
Thus,
The x-intercept are x = 0, x = -1.9, x = 0.35, and x = 1.5.
The local minimum is 1.
Increasing intervals are (-1.5, 0.5) and (1, ∞).
Decreasing intervals are (∞, -1) and (0, 1.5).
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Answer:
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Step-by-step explanation:
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Answer:
y = - 5
Step-by-step explanation:
locate x = - 1 on the x- axis, go vertically down to meet the line at (- 1, - 5 )
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2.87x7.8
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= 22.386
Hope this helps!
2.87 * 7.8
= 22.386
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Answer:
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Step-by-step explanation:
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[tex]GeniusUser[/tex]
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
First, you lay it down like this:
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Answer:
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Answer:
Step-by-step explanation:
In football, a gain is when a player moves the ball closer to the goal line; whereas, a loss is when the player loses yardage making it difficult to score. Larry plays quarterback for the Eagles. During the team's opening football game, the Eagles have the ball 48 yards away from the goal line. On the first play, the Eagles gain 31 yards on a pass toward the goal line. On the next four plays, the Eagles lose 3, 5, 7, and 4 yards, respectively. What is the distance between the ball and the goal line after these five plays?
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Answer:
36 yards
Step-by-step explanation:
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Given:
Eagles have the ball 48 yards away from the goal line.
On the first play, the Eagles gain 31 yards on a pass toward the goal line. On the next four plays, the Eagles lose 3, 5, 7, and 4 yards.
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