Math 121
Semester Exam Study Guide
Solutions
1) Factor 
2) Factor 
3) Factor
4) Factor
5) Solve 
6) Solve 
7) Solve 
8) Solve 
9) Find the
inverse of 
and graph f and f -1
10) Determine if the lines given
by the equations are parallel or perpendicular.
12) Find the
center and the radius of a circle with the given equation.
- 
13) Graph 
14) Given 
, find 
15) Find the
slope of the tangent line to 
passing through the
point at (1,-5)
16) Given
the revenue function 
, find the marginal revenue at x =100.
17) Evaluate
18) Evaluate
19) Evaluate
The limit does not
exist
20) Given 
, find the derivative of y.
21) Given 
find 
22) Find the first and second derivative of 
23) Given 
, find
24) Given 
, find
25) Discuss
the continuity of 
26) Discuss
the continuity of 
27) Find the
distance between the points (1,1) and (3,5)
28) Given , find f(3) and f(-1)
29) Given 
,find 
30) Use the first derivative test to find the intervals
where the function is increasing or decreasing
|
Interval |
|
|
|
|
Test Value |
x = -2 |
x = 0 |
x = 2 |
|
Sign of |
Positive |
Negative |
Positive |
|
Conclusion |
Increasing |
Decreasing |
Increasing |
31)
Find all extrema points of the function and discuss the concavity of the
function.
|
Interval |
|
|
|
|
Test Value |
x=-1 |
x=1 |
x=11 |
|
Sign of |
Positive |
Negative |
Positive |
|
Conclusion |
Increasing |
Decreasing |
Increasing |
Concavity
Test
|
Interval |
|
|
|
Test Value |
x=4 |
x=6 |
|
Sign of |
Negative |
Positive |
|
Conclusion |
Concave Down |
Concave up |
Extrema Points: Relative Maximum at x = 0 and a Relative Minimum x = 10
32)
Find all extrema points of the function and discuss
the concavity of the function.
Solution: The function has an inflection point at x=0
Concavity: Concave Up:
Concave Down : 
33)
34)
