The temperature was changing at a rate of 2.925 degrees Celsius in 2005
<h3>How to determine the rate in 2005</h3>From the graph (see attachment), we have the following ordered pair
(x,y) = (5,14.625)
The above means that, the temperature in 2005 is 14.625 degrees Celsius
So, the rate in 2005 is:
Hence, the temperature was changing at a rate of 2.925 degrees Celsius in 2005
Read more about average rates at:
Simplify the integrands by polynomial division.
Now computing the integrals is trivial.
5.
where we use the power rule,
and a substitution to integrate the last term,
8.
using the same approach as above.
Answer:
"I can find the maximum or minimum by looking at the factored expression of a quadratic function by reading off its roots and taking the arithmetic average of them to obtain the -coordinate of the quadratic function, and then substituting that value into the function."
Step-by-step explanation:
Because of the symmetry of quadratics (which is the case here because we have two factors of degree 1, so we are dealing with a <em>polynomial</em> of degree 2, which is a fancy way of saying that something is a quadratic), the -coordinate of the extremum (a fancy way of saying maximum or minimum) is the (arithmetic) average of the two roots.
In the factored form of a quadratic function, we can immediately read the roots: 3 and 7. Another way to see that is to solve , which gives
(the 'V' stands for 'or'). We can take the average of the two roots to get the
-coordinate of the minimum point of the graph (which, in this case, is
).
Having the -coordinate of the extremum, we can substitute this value into the function to obtain the maximum or minimum point of the graph, because that will give the
-coordinate of the extremum.