(a)
We have been given an equation
. Upon taking derivative of this equation with respect to x on both the sides, we get:

(b)
In order to write the equation of tangent line, we need to find the slope of the line. We know that point (3,11) lies on the graph. Therefore, we write the slope of the tangent as:

Therefore, equation of tangent line is:

(c)
We know that slope of tangent is given as
. The tangent will be vertical when denominator of slope is zero, that is:

The type of homeostatic regulation that is best described by the physiological responses of Jared would be the extrinsic regulation. It is the homeostatic regulation that results from the endocrine system and the nervous system activities. These organ systems are responsible of controlling a number of activities in the body simultaneously.<span />
This questions seems to be a question where you are required to mention more than one point. The question has two options of course, I'll tell you my personal answer to the question in broken up points.
I disagree with this statement because I believe that Physical Education (PE) is a very important subject for each individual.
It has been proven that any sort of physical education improves the activity of your brain, if an individual's level of brain activity is higher, it means he learns more from other education and performs better on his tests.
Physical Education is also a practical lesson that relieves stress off students from all the other core subjects that do not that involve as much practical activity.
Physical Education makes you healthier, the healthier you are the better your life style and (technically) life time will be.
Physical Education is also now proven to wake up students, this means students are less lazy and goes back to one of my previous points mentioning a students activity and performance in a lesson or a test.
I hope this helped, any other questions let me know. :3
Answer:
Ethnic rivalries caused unrest within independent nations. This meant that to ensure stability, the government of the day had to be authoritarian. This political environment emanating from the ethnic rivalry was largely to blame for the rise of authoritarian rule.