The graph of the function f(x) = –(x + 6)(x + 2) is shown below.
1 answer:
Answer:
Option A. x < -4
Step-by-step explanation:
The given function is f(x) = -(x + 6)(x + 2)
General form of the function will be,
f(x) = -(x² + 2x + 6x + 12)
= -(x² + 8x + 12)
Vertex form of the function will be,
f(x) = -[x² + 2(4)x + 12]
= -[(x² + 2(4)x + 16) - 16 + 12]
= -(x + 4)² + 4
Therefore, parabola for the function above will open down with vertex (-4, 4) as shown in the graph attached.
Graph shows the function is increasing in x < -4 and decreasing in x > -4.
Therefore, Option A. is the correct answer.
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Answer:
a) h = 123/x^2
b) S = x^2 +492/x
c) x ≈ 6.27
d) S'' = 6; area is a minimum (Y)
e) Amin ≈ 117.78 m²
Step-by-step explanation:
a) The volume is given by ...
V = Bh
where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:
123 = x^2·h
h = 123/x^2
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b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.
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c) The derivative of the area with respect to x is ...
When this is zero, area is at an extreme.
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d) The second derivative is ...
This is positive, so the value of x found represents a minimum of the area function.
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e) The minimum area is ...
The minimum area of metal used is about 117.78 m².