A circle is divided into 9 equal parts. What is the angle measured of two of those parts?What is the degrees
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<span>This tells us two things. Our slope is 3 and our y intercept is -4.
This tells us that we need to start at (0,-4).
Plot that point.
Since our slope is 3 (3/1), move up 3 and right 1.
This you will end up at point (1,-1).
Connect these two points in a straight line, and you have graphed your line.
It will look like this</span>
This tells us that we need to start at (0,-4).
Plot that point.
Since our slope is 3 (3/1), move up 3 and right 1.
This you will end up at point (1,-1).
Connect these two points in a straight line, and you have graphed your line.
It will look like this</span>
A) 
is continuous, so 
is also continuous. This means if we were to integrate 
, the same constant of integration would apply across its entire domain. Over 
, we have 
. This means that
For to be continuous, we need the limit as 
to match 
. This means we must have
Now, over
, we have 
, so 
, which means 
.
b) Integrating over [1, 3] is easy; it's just the area of a 2x2 square. So,
c) is increasing when 
, and concave upward when 
, i.e. when is also increasing.
We have
over the intervals 
and 
. We can additionally see that 
only on and .
d) Inflection points occur when
, and at such a point, to either side the sign of the second derivative 
changes. We see this happening at 
, for which 
, and to the left of we have decreasing, then increasing along the other side.
We also have along the interval 
, but even if we were to allow an entire interval as a "site of inflection", we can see that to either side, so concavity would not change.
For
Now, over
b) Integrating over [1, 3] is easy; it's just the area of a 2x2 square. So,
c)
We have
d) Inflection points occur when
We also have