Basic Rules of Applications Short Answers Flashcards
standard approximation for Δf
Δf ≈ f’_0Δx
standard approximation for f_1
f_1 ≈ f_0 + f’_0Δx
equation for a linear approxiamtion of f
L(x) = f_0 + f’_0Δx or L(x) = f_0 + f’_0(x_1-x_0)
When is the linear approximation accurdate?
Near x_0
whats the difference between a linear approximation and an f_1 approxiatmion
x_1 is left as x
What do curves with deriation look like when you zoom in on them?
a straight line
whats the relationship between the graph of as function and the graph of one ofits linear approximations
the linear approximation is a tangent line
Intuitively what is f’(x)?
f ‘s per x
What is the value of Seconds’(Minute)?
60
Intuitively why is 20’ = 0
20 never changes. It’s a constant
Write “if one worker makes 20 widgets per hour, then 3
workers make 320 widgets” in symbolic notation.
(3𝑊(ℎ))′ =3𝑊′(ℎ)
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.
(𝐻(𝑦)+𝑊(𝑦))′ =𝐻′(𝑦)+𝑊′(𝑦)
What happens to the graph of a function when you add a number to the function?
The graph goes up.
What happens to the slope of a function when you add a number to the function?
Nothing. It’s the same slope just higher.
Leibnitz is more of an _________ than an __________.
Enigma, Explanation
Write “the number of feet per feet is 1” in symbolic
notation.
x’ = 1
You can only plug in a number _________ you take a
derivative.
after
What is (𝑥^𝑛)′
𝑛𝑥^𝑛−1
What does 𝑑𝑦/ 𝑑𝑥|𝑥=2 mean?
Take the derivative of y and then plug in a 2.
Translate f has a horizontal slope at x into symbols.
𝑓 ′(𝑥)=0
Translate f and g have the same slope at x into symbols.
𝑓 ′(𝑥)=𝑔′(𝑥)
What does Miles′(Gallon) represent?
Miles per gallon
Express Yen per Dollar in function form.
Yen′ (Dollar)
You’re solving for the price in dollars per pound. When
you take a derivative, what variable has a derivative
of 1?
P = pounds
You’re solving for the mileage in miles per gallon.
When you take a derivative, what variable has a
derivative of 1?
G = gallons
What’s average $ per £ (dollars per pound)
symbolically.
Δ$/Δ£
What is marginal $ per £ (dollars per pound)
symbolically
$′(£)
What does the Intermediate value theorem say about the Turnpike?
If you drive from Exit 8 to 10 on the Turnpike, you pass exit 9
What property must the function have to satisfy the
Intermediate Value Theorem?
Continuity
