Rates of Change and Monotonicity — Quiz

The radius of a circular ripple grows at

3

cm/s. How fast is its area growing when the radius is

5

cm?

A

15\pi

cm²/s

B

10\pi

cm²/s

C

30\pi

cm²/s

D

75\pi

cm²/s

A cube's edge grows at

0.5

cm/s. How fast is its volume growing when the edge is

4

cm?

A

24

cm³/s

B

48

cm³/s

C

8

cm³/s

D

32

cm³/s

The revenue from selling

x

units is

R(x) = 3x^2 + 20x + 5

. Find the marginal revenue at

x = 10

.

A

50

B

505

C

60

D

80

On which interval is

f(x) = x^3 - 3x^2 - 9x + 5

decreasing?

A

(-\infty, -1)

B

(-1, 3)

C

(-3, 1)

D

(3, \infty)

The function

f(x) = e^{-x}

is

A decreasing on

\mathbf{R}

B constant

C increasing on

(0, \infty)

only

D increasing on

\mathbf{R}

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