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1 answer:
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Given:
The graph of a function .
To find:
The interval where .
Solution:
From the given graph graph it is clear that, the function before x=0 and after x=3.6 lies above the x-axis. So, for
and
.
The function between x=0 and x=3.6 lies below the x-axis. So, for
.
Now,
For , the graph of h(x) is above the x-axis. So,
.
For , the graph of h(x) is below the x-axis. So,
.
For , the graph of h(x) is below the x-axis. So,
.
Only for the interval , we get
.
Therefore, the correct option is A.
Answer:
(-∞, -2), (-2, -0.618), and (1.618, 3)
Step-by-step explanation:
The red arrows indicate the regions in which the function is decreasing.
The corresponding intervals are (-∞, -0.618) and (1.618, 3),
Let's examine the intervals given.
(-∞, -2): Yes, decreasing.
(-2, -0.618): Yes, decreasing.
(-2, 0.689): No. Decreasing in (-2, -0.618) but increasing in (-0.618, 0.689).
(-1.17, 0.689): No. Decreasing in (-1.17, -0.618) but increasing
in (-0.618, 0.689).
(0.698, 71.457): No. Increasing from (0.698, 1.618), decreasing in (1.618, 3) and increasing in (3, 71.457).
(1.618, 3): Yes, decreasing.
(2.481, ∞): No. Decreasing in (2.481, 3) but increasing in (3, ∞).
The three choices that indicate a decreasing interval are (-∞, -2),
(-2, -0.618), and (1.618, 3).
