Free Printable Review Unit 5 pt 2 (applications of derivatives)

Worksheets

Review Unit 5 pt 2 (applications of derivatives)

Total questions: 19

Worksheet time: 2hrs 38mins

Name

Class

Date

Find dy for the function y = 4x²+ x + 3.

(8x²+ x + 3)dx

(4x + 1)dx

(8x + 1)dx

8x + 1

Find dy for 2xy²- x² +y = 5 if x = 0 and dx = 0.01.

-50

-0.5

-5

(2x - 2y²) / (4xy + 1) dx

The linearization of function y=f(x) near the value x=a is given by:

L(x) = f(a) + f'(a) (x - a)

L(a) = f(x) + f'(x) (x - a)

L(x) = f'(a) + f(a) (x - a)

L(a) = f'(x) + f(x) (x - a)

Let f(x) = x³and L(x) be the linearization of f(x) centered at x = 2. Find L(x).

L(x) = 12x - 16

L(x) = 12x - 8

L(x) = 8 - 12(x - 2)

L(x) = 12x + 32

Let f(x) = x³and L(x) be the linearization of f(x) centered at x = 2. Calculate the approximation for f(2.1).

9.3

9.261

9.2

Let f(x) = x³and L(x) be the linearization of f(x) centered at x = 2. Calculate the approximation error when ∆x = 0.1.

0.1

0.01

0.661

0.061

Let L(x) = 3(x - 4) - 2. Find L(3.9).

-1.7

-2.3

2.3

What is the differential equation, $dy=f'(x)dx$ , for $\sqrt{52}$

$dy=3$

$dy=\frac{3}{14}$

$dy=\frac{1}{14}$

$dy=\frac{1}{7}$

What is the decimal approximation of $\sqrt{52}$ using $dy=f'(x)dx$

7.2111

$\frac{3}{14}$

10.5

7.214

10.

If y=2x-8, what is the minimum value of the product xy?

-16

-8

-4

11.

Find the smallest perimeter for a rectangle with an area of 256 in².

128

12.

A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

100ft x 200ft

102ft x 196 ft

50 ft x 300 ft

50 ft x 175 ft

13.

The volume of a cylindrical tin can with a top and a bottom is to be 16π cubic inches. If a minimum amount of tin is to be used to construct the can, what must be the height, in inches, of the can?

2 ³√2

2√2

2 ³√4

14.

We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft³, determine the dimensions that will minimize the amount of material used.

w=2.027ft, h=4.055ft, l=6.082ft

w=1.488ft, h=3.347ft, l=6.694ft

w=2.231ft, h=3.347ft, l=6.694ft

w=0.485ft, h=2.111ft, l=4.222ft

15.

Select each true statement(s) that pertain to this situation:

Water is filling a circular cone shape tank measured in cubic centimeters per minute.

V(t) represents the rate at which water is being pumped in

V'(t) represents the rate at which water is being pumped in

$\frac{dr}{dt}$ represents the water level's rate

$\frac{dh}{dt}$ represents the water level's rate

At t = 1 would show the rate at which the water level is increasing after 1 minute

16.

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec. How fast is the height of the water changing when the water is 2 ft deep?

$\frac{-9}{8\pi}$ ft/sec

$\frac{9}{8\pi}$ ft/sec

$\frac{-8}{9\pi}$ ft/sec

$\frac{8}{9\pi}$ ft/sec

17.

A boat is being pulled into dock by means of a winch 12 feet above the deck of the boat. Suppose the boat is moving at a constant rate of 4 feet per second. Determine the speed at which the winch pulls in rope when there is a total of 13 feet of rope out.

2.32 ft/s

-1.54 ft/s

12.2 ft/s

-4.32 ft/s

18.

Brandon is starting to clean up after a birthday party. He begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm³/sec. How fast is the diameter changing when the diameter is 8 cm?

$\frac{-1}{16\pi}$ cm/sec

$\frac{-1}{16}$ cm/sec

$\frac{-1}{4\pi}$ cm/sec

$\frac{1}{4\pi}$ cm/sec

19.

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

3 ft/sec

-7.2 ft/sec

7.2 ft/sec

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Review Unit 5 pt 2 (applications of derivatives)

Total questions: 19

Worksheet time: 2hrs 38mins

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