The price of one share of a company’s stock declined $13.89 every day for 2.5 days. What was the stock’s total decline in price?
2 answers:
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Answer:
- range: (-∞, 29.4336]
- min: -∞
- max: 29.4336
Step-by-step explanation:
I found these using a graphing calculator. (See attached)
The function is a polynomial of 4th degree with a negative leading coefficient. (The coefficient of the 4th-degree term is -3.) Therefore, it opens downward and has a range that extends to -∞. This function only has one global maximum and no local minimum.
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The maximum can be found by solving the cubic equation that results from taking the derivative of this function and finding the root of that:
df/dx = -12x^3 -2x -20 = 0
There are formulas for the solutions of a cubic, but the one negative real root of this cubic can be found easily with a graphing calculator using iteration:
x ≈ -1.13879908894.
Dividing by -2, the above derivative function can be written as ...
g(x) = 6x^3 +x +10
The one real zero of it can be found using Newton's Method iteration.
The Newton's Method iterator function is
h(x) = x - g(x)/g'(x)
where g'(x) is the derivative of g(x), often available as a function on the graphing calculator.
The starting value for the iteration can be the x-value obtained from the graph: -1.139. It only takes about 2 or 3 iterations to find x to the precision of the calculator: x = h(h(x)). This x is the x-coordinate of the maximum, so f(x) is the maximum value: 29.4335546516.
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The attachments show the function definitions and their use for finding the maximum of f(x) using a TI-84 calculator. Y₁ is the function f(x); Y₂ is its derivative, shown above as g(x). Y₃ is the iterating function, shown above as h(x). The nDeriv( ) function is a calculator function that finds the numerical derivative of its argument.
Answer:
180
Step-by-step explanation:
At the beggining, it says they are stacked in 5 layers which means the number of cubes is divisible by 5.
If the number of cubes equals x:
The least amount of sugar cubes the Jones family could have used is which equals 122. The most they couldve used is
which equals 183.
Based on the information from the Jones family, x is between 122 and 183.
Based on the information from the Connor's, x is between 176 and 264.
Based on the information from both, x is between 176 and 183. The only number that is divisible by 5 between those numbers is 180 cubes.