Free Printable 2.4-2.7 More Derivative Review

1.

If H(x) = f ^-1(x), then H'(3) equals

a)

4

b)

1/4

c)

- 1/4

d)

-4

2.

Find dy/dx at a given point.

a)

5/4

b)

4/5

c)

1

d)

-5

3.

Find the derivative of the inverse

a)

12

b)

1/12

c)

146

d)

1/146

4.

find y'

a)

A

b)

B

c)

C

d)

D

5.

Find dy/dx:

$y=\ln\left(5x^2\right)$

a)

$\frac{2}{x}$

b)

$\frac{1}{10x}$

c)

$\frac{1}{5x^2}$

d)

$5x^2$

6.

Find the Derivative

a)

A

b)

B

c)

C

d)

D

7.

Find h'(3)

a)

-2

b)

0

c)

1

d)

3

8.

Use implicit differentiation to find y' for the following equation: 4x cos(y) = 1

a)

y' = cos(y) / x sin(y)

b)

y' = 4x sin(y)

c)

y' = cot(y)

d)

y' = 4 / sec(y)tan(y)

9.

A cube shrinks so that the length of its sides are decreasing at a rate of 4 m/min. At what rate is the volume of the cube changing when the sides are 5 m each?

a)

-296 m³/min

b)

-297 m³/min

c)

-300 m³/min

d)

-307 m³/min

10.

Find y'' for y = 3x² + 5x + cos x

a)

f''(x) = 6x + cos x

b)

f''(x) = 3x + 5 - sin x

c)

f''(x) = 6x + 5 + sin x

d)

f''(x) = 6 - cos x

11.

a)

Only the Quotient Rule

b)

The Quotient and Product Rules

c)

The Quotient and Chain Rules

d)

Only the Chain Rule

12.

Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 3 cm/min. How fast is the area of the pool increasing when the radius is 12 cm?

a)

$76\pi\ \frac{cm^2}{\min}$

b)

$72\pi\frac{cm^2}{\min}$

c)

$77\pi\frac{cm^2}{\min}$

d)

$62\pi\frac{cm^2}{\min}$

13.

$\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$

a)

$5x^2$

b)

$10x$

c)

10

d)

DNE

14.

a)

A

b)

B

c)

C

d)

D

15.

a)

A

b)

B

c)

C

d)

D

16.

a)

A

b)

B

c)

C

d)

D

17.

A tank is being filled with a liquid. The function V gives the volume of liquid in the tank, in liters, after t minutes.

What is the best interpretation for the following statement?

The value of the derivative of V at t=1 is equal to 2.

a)

After 1 minute, the tank was being filled at a rate of 2 liters.

b)

After 1 minute, the tank had 2 liters of liquid.

c)

After 1 minute, the tank was being filled at a rate of 2 liters per minute.

d)

During the first minute, the tank was being filled at a rate of 2 liters per minute.

18.

This table gives select values of the differentiable function g

What is the best estimate for g'(-9) we can make based on this table?

a)

1.57

b)

-34

c)

2

d)

2/3

19.

Find dy/dx if $3x^2+6y^2+10=5x+7y+100$

a)

$\frac{dy}{dx}=\frac{-6x+5}{12y-7}$

b)

$\frac{dy}{dx}=\frac{-6x+5}{-12y+7}$

c)

$\frac{dy}{dx}=\frac{6x-5}{12y-7}$

d)

$\frac{dy}{dx}=\frac{-3x+5}{6y-7}$

e)

$\frac{dy}{dx}=\frac{3x-5}{6y-7}$

20.

If $y=\tan^{-1}\left(\cos\ x\right)$ , then $\frac{\text{d}y}{\text{d}x}$ =

a)

$\left(\sec^{-1}\left(\cos\ x\right)\right)^2$

b)

$\frac{1}{\left(\cos^{-1}x\right)^2+1}$

c)

$-\left(\sec^{-1}\left(\cos x\right)\right)^2\sin x$

d)

$\frac{-\sin x}{1+\cos^2x}$

21.

For what values of x does $y^2-2x^3-12x^2=0$ have horizontal tangent lines?

a)

x = 0 only

b)

x = 0 and x = - 4

c)

x = - 4 only

d)

x = - 4, x = 0, and x = 4

22.

$x^2+xy+y^2=9\ @\ \left(1,2\right)$ Use implicit differentiation to write the equation of the tangent line to the curve at the given point.

a)

$y-1=\frac{-4}{5}\left(x-2\right)$

b)

$y-2=\frac{-4}{5}\left(x-1\right)$

c)

$y-2=\frac{4}{5}\left(x-1\right)$

d)

$y+2=\frac{-4}{5}\left(x+1\right)$

23.

Find $h'\left(-4\right)$

a)

-4

b)

-1/4

c)

1/4

d)

4

24.

The table gives values of the rate of change of the radius of the balloon, r(t), measured in feet per minute. What would the units be if you found r'(9)

a)

ft

b)

ft/min

c)

ft/min^2

d)

min/ft

25.

Grass clippings are placed in a bin where they decompose. For 0 < t < 30, the rate of decomposition of the grass is modeled by A(t), where A is measured in pounds per day. If we know that A'(15) = 5, is the following a correct interpretation of A'(15)?

The rate of decomposition is INCREASING by 5 pounds per day per day after the 15th day.

a)

Correct

b)

Incorrect

26.

The temperature of coffee in a cup at time t minutes is modeled by the function, where C(t) is measured in degrees Celsius. If C'(3) = -4, is the following a CORRECT interpretation of C'(3) is context?

The TEMPERATURE OF THE COFFEE is DECREASING by 4 degrees Celsius/minute

a)

Completely Correct

b)

Incorrect

27.

Water is pumped into a tank at a rate modeled by W(t) liters per hour, where t is measured in hours. If you found W'(t), the units would be...

a)

liters

b)

liters/hr

c)

liters/hr^2

d)

hrs/liter

28.

If s(t) represents the meters traveled in t minutes, s'(t) would represent...

a)

meters

b)

meters/min

c)

meters/min^2

d)

min/meters

29.

Car A is traveling west at 50 mi/hr and car B is traveling north at 60 mi/rh. Both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 0.3 mi and car B is 0.4 mi from the intersection?

a)

78 mi/hr

b)

38 mi/hr

c)

68 mi/hr

d)

54 mi/hr

2.4-2.7 More Derivative Review

Total questions: 29

Worksheet time: 2hrs 36mins

Similar Resources on Wayground