If 2000 is placed into a bank account that pays 3% compound interest per year how much will be in the account after 2 years
1 answer:
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The given polynomial function has 1 relative minimum and 1 relative maximum.
<h3>What are the relative minimum and relative maximum?</h3>- The relative minimum is the point on the graph where the y-coordinate has the minimum value.
- The relative maximum is the point on the graph where the y-coordinate has the maximum value.
- To determine the maximum and the minimum values of a function, the given function is derivated(since the maximum or minimum is obtained at slope = 0)
The given function is
f(x) = 2x³ - 2x² + 1
derivating the above function,
f'(x) = 6x² - 4x
At slope = 0, f'(x) = 0 (for maximum and minimum values)
⇒ 6x² - 4x = 0
⇒ 2x(3x - 2) = 0
2x = 0 or 3x - 2 = 0
∴ x = 0 or x = 2/3
Then the y-coordinates are calculated by substituting these x values in the given function,
when x = 0;
f(0) = 2(0)³ - 2(0)² + 1 = 1
So, the point is (0, 1)
when x = 2/3;
f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27
So, the point is (2/3, 19/27)
Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.
So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.
Thus, option A is correct.
Learn more about the relative minimum and maximum here:
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We have a square garden of 400 square foot.
The area of a square is:
where x: side length.
In this case:
The perimeter of the square is the sum of the lengths of the sides of the square. As they are all equal, we can write:
The fencing is priced at $1.50 per foot. If we add the 7% sales tax to this price we get:
The fencing will be installed in all the perimeter (80 ft).
We can calculate the total cost by multiplying the sales price ($1.605 per foot) and the perimeter (80 ft):
Answer: the fencing will cost a total of $128.40