Basic Rules of Applications Short Answers

Question 1

standard approximation for Δf

Answer 1

Δf ≈ f’_0Δx

Question 2

standard approximation for f_1

Answer 2

f_1 ≈ f_0 + f’_0Δx

Question 3

equation for a linear approxiamtion of f

Answer 3

L(x) = f_0 + f’_0Δx or L(x) = f_0 + f’_0(x_1-x_0)

Question 4

When is the linear approximation accurdate?

Answer 4

Near x_0

Question 5

whats the difference between a linear approximation and an f_1 approxiatmion

Answer 5

x_1 is left as x

Question 6

What do curves with deriation look like when you zoom in on them?

Answer 6

a straight line

Question 7

whats the relationship between the graph of as function and the graph of one ofits linear approximations

Answer 7

the linear approximation is a tangent line

Question 8

Intuitively what is f’(x)?

Answer 8

f ‘s per x

Question 9

What is the value of Seconds’(Minute)?

Answer 9

60

Question 10

Intuitively why is 20’ = 0

Answer 10

20 never changes. It’s a constant

Question 11

Write “if one worker makes 20 widgets per hour, then 3
workers make 320 widgets” in symbolic notation.

Answer 11

(3𝑊(ℎ))′ =3𝑊′(ℎ)

Question 12

Write “if a husband makes $60K per year and his wife
makes $50K per year then together they make
60+50K per year” in symbolic notation.

Answer 12

(𝐻(𝑦)+𝑊(𝑦))′ =𝐻′(𝑦)+𝑊′(𝑦)

Question 13

What happens to the graph of a function when you add a number to the function?

Answer 13

The graph goes up.

Question 14

What happens to the slope of a function when you add a number to the function?

Answer 14

Nothing. It’s the same slope just higher.

Question 15

Leibnitz is more of an _________ than an __________.

Answer 15

Enigma, Explanation

Question 16

Write “the number of feet per feet is 1” in symbolic
notation.

Answer 16

x’ = 1

Question 17

You can only plug in a number _________ you take a
derivative.

Answer 17

after

Question 18

What is (𝑥^𝑛)′

Answer 18

𝑛𝑥^𝑛−1

Question 19

What does 𝑑𝑦/ 𝑑𝑥|𝑥=2 mean?

Answer 19

Take the derivative of y and then plug in a 2.

Question 20

Translate f has a horizontal slope at x into symbols.

Answer 20

𝑓 ′(𝑥)=0

Question 21

Translate f and g have the same slope at x into symbols.

Answer 21

𝑓 ′(𝑥)=𝑔′(𝑥)

Question 22

What does Miles′(Gallon) represent?

Answer 22

Miles per gallon

Question 23

Express Yen per Dollar in function form.

Answer 23

Yen′ (Dollar)

Question 24

You’re solving for the price in dollars per pound. When
you take a derivative, what variable has a derivative
of 1?

Answer 24

P = pounds

Question 25

You’re solving for the mileage in miles per gallon.
When you take a derivative, what variable has a
derivative of 1?

Answer 25

G = gallons

Question 26

What’s average $ per £ (dollars per pound)
symbolically.

Answer 26

Δ$/Δ£

Question 27

What is marginal $ per £ (dollars per pound)
symbolically

Answer 27

$′(£)

Question 28

What does the Intermediate value theorem say about the Turnpike?

Answer 28

If you drive from Exit 8 to 10 on the Turnpike, you pass exit 9

Question 29

What property must the function have to satisfy the
Intermediate Value Theorem?

Answer 29

Continuity