Answer:
The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.
Step-by-step explanation:
Let 
, for 
. 
represents the temperature of the water, measured in degrees Celsius, and 
is the number of salmon swimming upstream to spawn, dimensionless.
We compute the first and second derivatives of the function:
(Eq. 1)
(Eq. 2)
Then we equalize (Eq. 1) to zero and solve for :
And all roots are found by Quadratic Formula:
, 
Only the first root is inside the given interval of the function. Hence, the correct answer is:
Now we evaluate the second derivative at given result. That is:
According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.
Answer:
Relationship between temperature at different times of the day during the Winter period in places like Alaska and Minnesota in the USA.
Step-by-step explanation:
An example of a relationship that would have a negative number in the domain or range would be the relationship between the temperature at different times of the day during the snow period in the winter. It's well known that in places like Alaska and Minnesota in the USA, that during the winter when there's very heavy snow, the average temperature is usually below 0°C. The temperature is the dependent variable and is most likely negative in those 2 states and thus the range would have negative numbers.
X^2 - 14x + 42 = 0
x^2 - 14x = -42
x^2 - 14x + 49 = 49 - 42
(x - 7)^2 = 7
x - 7 = (+-) sqrt 7
x = 7 (+-) sqrt 7
solutions are : x = 7 + sqrt 7 and x = 7 - sqrt 7
