Application of Derivatives — Course Quiz

Find the rate of change of the area of a circle with respect to its radius when

r = 6

cm.

A

12\pi

cm²/cm

B

24\pi

cm²/cm

C

6\pi

cm²/cm

D

36\pi

cm²/cm

A balloon's radius grows at

0.2

cm/s. How fast is its volume growing when

r = 5

cm?

A

100\pi

cm³/s

B

20\pi

cm³/s

C

\displaystyle \tfrac{20\pi}{3}

cm³/s

D

4\pi

cm³/s

The cost of making

x

items is

C(x) = 2x^2 + 5x + 100

. Find the marginal cost at

x = 10

.

A

40

B

350

C

25

D

45

On which interval is

f(x) = 2x^3 - 24x + 1

decreasing?

A

(-4, 4)

B

(-\infty, -2)

C

(-2, 2)

D

(2, \infty)

The function

f(x) = \log x

is

A increasing on

(0, \infty)

B decreasing on

(0, \infty)

C decreasing on

(0, 1)

and increasing on

(1, \infty)

D increasing on

\mathbf{R}

Find the local minimum value of

\displaystyle f(x) = x + \dfrac{9}{x}

for

x > 0

.

A

9

B

6

C

10

D

3

At

x = 0

, the function

f(x) = x^3

has

A an absolute minimum

B neither a maximum nor a minimum

C a local maximum

D a local minimum

Find the absolute minimum of

f(x) = x^3 - 3x

on

[0, 2]

.

A

-2

B

2

C

0

D

-3

An open box is made from an

18

cm square sheet by cutting equal squares of side

x

from the corners. Which

x

gives the largest volume?

A

3

cm

B

4.5

cm

C

9

cm

D

6

cm

A wire

28

cm long is bent into a rectangle. What is the largest area it can enclose?

A

196

cm²

B

49

cm²

C

48

cm²

D

56

cm²

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Application of Derivatives — Course Quiz

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