4 problems about related rates, linear approximation and differential, and maximum and minimum values

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MATH 211

Learning Activity – Related Rates (Continued)

Fall 2017

Name:

1. A boat is pulled toward a dock by a rope from the bow through a ring on the dock 6 ft above the

bow. The rope is hauled in at the rate of 2 ft/sec.

(Let θ be the angle between the rope and the dock (in radians).)

(a) How fast is the boat approaching the dock when 10 ft of rope are out?

(b) At what rate is the angle between the rope and the dock changing then?

MATH 211

Learning Activity – Linear Approximation and Differentials

Fall 2017

Name:

1. Approximate the change in the volume of a sphere when its radius changes from r = 5ft to r = 5.1ft.

4

Use V (r) = πr3 .

3

2. Find a linear approximation of f (x) =

√

3

x at x0 = 26.8.

MATH 211

Learning Activity – Linear Approximation and Differentials

Fall 2017

4+x

. Express the relationship between a small change in x and the corresponding

4−x

change in y in the form dy = f 0 (x)dx.

3. Let f (x) =

MATH 211

Learning Activity – Maximum and Minimum Values

Fall 2017

Name:

1. Identify the local and absolute extreme values on the graph of f (x). Fill in the blanks with absolute

max, absolute min, local min, local max, or not extreme.

a–

b–

Text

p–

q–

r–

s–

t–

2. Find the critical points of f (x) = 2×2 + 10x

28 on the interval [ 2, 10].

MATH 211

Learning Activity – Maximum and Minimum Values

3. Match graphs that have the following characteristics:

(a) Continuous on (a, b) but has neither a local max nor a local min.

(b) Has an absolute max, a local min, but no absolute min.

(c) Has a local min where f 0 (x) = 0.

(d) Has a local min where f 0 (x) is not defined.

Fall 2017

…

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