Find all local and global extrema!!! HELP NEEDED!!!
1 answer:
Answer:
The local and global extrema are: (-3,0), (0,-1.62), and (3,0)
Step-by-step explanation:
To solve this, we can use a graphing calculator.
The graph of the function looks as it is shown on the image.
Local extrema is defined as the highest/lowest y-value in a general area, while global extrema are the highest/lowest defined y-value on the function.
This graph shows that the highest points (as it is tied at y=0) are (-3,0) and (3,0), so they would be both local and global maximum.
Additionally, the local min is seen to be at (0,-1.62). This is also a global minimum as this function is not given a defined domain, so it can be assumed that the domain of this function is (-∞,∞). Global extrema can only occur at defined values, so the end points of -∞ and ∞ can be ignored.
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Answer:
The given sequence 6, 7, 13, 20, ... is a recursive sequence
Step-by-step explanation:
As the given sequence is
- It cannot be an arithmetic sequence as the common difference between two consecutive terms in not constant.
As
,
As d is not same. Hence, it cannot be an arithmetic sequence.
- It also cannot be a geometrical sequence and exponential sequence.
It cannot be geometric sequence as the common ratio between two consecutive terms in not constant.
As
,
,
As r is not same, Hence, it cannot be a geometric sequence or exponential sequence. As exponential sequence and geometric sequence are basically the same thing.
So, if we carefully observe, we can determine that:
- The given sequence 6, 7, 13, 20, ... is a recursive sequence.
Please have a close look that each term is being created by adding the preceding two terms.
For example, the sequence is generated by starting from 1.
and
for n > 1.
<em>Keywords: sequence, arithmetic sequence, geometric sequence, exponential sequence</em>
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