Given f '(x) = (2 - x)(6 - x), determine the intervals on which f(x) is increasing or decreasing. (2 points)
Decreasing (-∞, 2); increasing on (6, ∞)
Decreasing (2, 6); increasing on (-∞, 2) U (6, ∞)
Decreasing (-∞, 2) U (6, ∞); increasing on (2, 6)
Increasing (-∞, -2) U (-6, ∞); increasing on (-2, -6)

Answers

Answer 1

Answer:

Decreasing (2, 6); increasing on (-∞, 2) U (6, ∞)

Step-by-step explanation:

To determine where [tex]f(x)[/tex] is increasing or decreasing, we set [tex]f'(x)=0[/tex] and check for the intervals.

We see that [tex]f'(x)=0[/tex] when either [tex]x=2[/tex] or [tex]x=6[/tex]. Therefore, we'll need to check the intervals [tex](-\infty,2)[/tex], [tex](2,6)[/tex], and [tex](6,\infty)[/tex]

For the interval [tex](\infty,2)[/tex], we can pick [tex]x=0[/tex] . This means that[tex]f'(0)=(2-0)(6-0)=(2)(6)=12>0[/tex], showing that [tex]f(x)[/tex] increases on the interval [tex](-\infty,2)[/tex]

For the interval [tex](2,6)[/tex], we can pick [tex]x=4[/tex]. This means that [tex]f'(4)=(2-4)(6-4)=(-2)(2)=-4<0[/tex], showing that [tex]f(x)[/tex] decreases on the interval [tex](2,6)[/tex]

For the interval [tex](6,\infty)[/tex], we can pick [tex]x=7[/tex]. This means that [tex]f'(7)=(2-7)(6-7)=(-5)(-1)=5>0[/tex], showing that [tex]f(x)[/tex] increases on the interval [tex](6,\infty)[/tex]

Therefore, [tex]f(x)[/tex] is increasing on [tex](-\infty,2)\cup(6,\infty)[/tex] and is decreasing on [tex](2,6)[/tex].


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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

Step-by-step explanation:

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x = - 36/2

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Answer:

x = -18

Step-by-step explanation:

2x - 17 =  -53

    +17 = + 17            Add 17 to both sides

2x       =   -36            

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Answers

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Answer:

Step-by-step explanation:

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Step-by-step explanation: This is the answer

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Step-by-step explanation:

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Answers

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Answers

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Answers

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Step-by-step explanation:

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Answers

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Answers

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Answers

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Answers

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Step by step

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Answers

Answer:

He wrapped 3/4 of the cake.

Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

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Answers

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Answers

Answer:

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Step-by-step explanation:

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709
50
O
20
50
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70
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500
709
20
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Answers

Answer:

Step-by-step explanation:

Given :-

Two angles in a triangle have measurements of 20° and 50 °.

To Find  :-

Measurement of third angles of triangle

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We know that the sum of all angles of triangle is 180°.

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Answer:

The third option is the correct answer.

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