| |
| |
1. |
The function f(x) = 3x2 - x3 has critical points at x = 0 and x = 2. Determine whether each of these critical points is the location of a relative maximum, relative minimum, or a point of inflection. |
| |
|
A. |
None of these is correct. |
B. |
(0, 0) minimum and (2, 4) point of inflection |
| |
|
C. |
(0, 0) minimum and (2, 4) maximum |
D. |
(0, 0) maximum and (2, 4) minimum |
| |
|
Hint |
|
| |
2. |
Determine whether the given critical point of x = -7 is the location of a relative maximum, relative minimum, or a point of inflection for the function f(x) =  x3 +  x2 + 1. |
| |
|
A. |
maximum |
B. |
none is correct |
| |
|
C. |
minimum |
D. |
point of inflection |
| |
|
Hint |
|
| |
3. |
Use a graphing calculator to graph g(x) = x3 - x + 1 and to determine and classify its extrema. |
| |
|
A. |
relative maximum:
(-0.6, 1.38);
relative minimum:
(0.6, 0.62) |
B. |
relative minimum:
(-0.6, 1.38);
relative maximum:
(0.6, 0.62) |
| |
|
C. |
relative maximum:
(1.38, -0.6);
relative minimum
(0.6, 0.62) |
D. |
relative minimum:
(1.38, -0.6);
relative maximum:
(0.6, 0.62) |
| |
|
Hint |
|
| |
4. |
The function f(x) = -(x - 3)2 + 4 has a critical point at x = 3. Determine and classify this point. |
| |
|
A. |
(3,4) is the relative maximum of this function. |
| |
|
B. |
(3,4) is the absolute maximum of this function. |
| |
|
C. |
(3,4) is the absolute minimum of this function. |
| |
|
D. |
(3,4) is the point of inflection. |
| |
|
Hint |
|
| |
5. |
The function f(x) = - (x + 2)3 - 3 has a critical point at x = -2. Determine whether this is the location of a maximum, minimum or a point of inflection. |
| |
|
A. |
extremum |
| |
|
B. |
maximum |
| |
|
C. |
minimum |
| |
|
D. |
point of inflection |
| |
|
Hint |
|
|
|