MAT 117 - Arizona State University



MAT 210 Practice – First Derivative test and more.

1) Given the function f(x) = 5 – 6x – 3x2

a) Find all critical points.

b) List the intervals in which f(x) is increasing.

c) List the intervals in which f(x) is increasing.

d) List all of the points at which f(x) has a local maximum.

e) List all of the points at which f(x) has a local minimum.

2) Given the function [pic]

a) Find all critical points.

b) List the intervals in which f(x) is increasing.

c) List the intervals in which f(x) is increasing.

d) List all of the points at which f(x) has a local maximum.

e) List all of the points at which f(x) has a local minimum.

3) Given the function [pic]

a) Find all critical points.

b) List the intervals in which f(x) is increasing.

c) List the intervals in which f(x) is increasing.

d) List all of the points at which f(x) has a local maximum.

e) List all of the points at which f(x) has a local minimum.

4) Given the function [pic]

a) Find all critical points.

b) List the intervals in which f(x) is increasing.

c) List the intervals in which f(x) is increasing.

d) List all of the points at which f(x) has a local maximum.

e) List all of the points at which f(x) has a local minimum.

5) Given the function [pic]

a) Find all critical points.

b) List the intervals in which f(x) is increasing.

c) List the intervals in which f(x) is increasing.

d) List all of the points at which f(x) has a local maximum.

e) List all of the points at which f(x) has a local minimum.

6) Find all local extrema for f(x) = x3 – 3x2 + 3x – 4

7) Find all local extrema for f(x) = 2x3 – 9x2 – 24x + 11

Answers:

1a) Critical Points at -1

b) increasing on [pic]

c) decreasing on [pic]

d) local maximum at (-1, 8)

e) no local minimums

2a) Critical Points at 2

b) increasing on [pic]

c) decreasing on [pic]

d) local maximum at (2, 3)

e) no local minimums

3a) Critical Points at [pic]

b) increasing on [pic]

c) decreasing on [pic]

d) no local maximum

e) local minimum at [pic]

4a) Critical Points at -2, 0, 2

b) increasing on [pic]and (-2, 0)

c) decreasing on (0, 2) and [pic]

d) local maximum at (0, -1)

e) no local minimums

5a) Critical Points at [pic]

b) increasing on [pic]

c) decreasing on [pic]

d) local maximum at [pic]

e) no local minimum

6) No local extrema

7) Local maximum of 24 when x = -1

Local minimum of -101 when x = 4

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