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Interpretations of Derivatives
Miscellaneous
General Calculus
Limits
Derivatives
100

Name two different notations for the derivative.

What is  f '   or  

dy/dx

100

True or False: 

When the acceleration of a car is zero, the car is not moving.

False
100
Name three times when a limit does not exist.
1. f(x) approaches a different number from left and right side of c 2. f(x) increases or decreases without bound 3. f(x) oscillates between two fixed values
100
lim┬(x→-1)⁡ (x^2-1)/(x+1)
-2
100

What is the derivative of x4

4x3

200

Given a position function s=f(x), which describes the distance of a particle, in inches, at a given time, measured in seconds, from a starting point, describe the meaning, in words, of 

f'(2)=10

After two seconds, the particle is moving away from the starting point at a rate of 10 inches per second. 

200

True or False

A function can have a non-zero first derivative and a zero second derivative.

True

200
Name the three parts of calculus.
Limits Differentiation Integration
200
lim┬(x→-3)⁡ (x^2+x-6)/(x^2-9)
5/6
200

True or false:

A function can be differentiable at a point, but not continuous there.

False

300

If a laser printer takes T(P) minutes to produce P pages, how do we measure the derivative 

(dP)/(dT)

minutes per page

300

What is the punishment for calling yourself the S word in Ms. Meg's class?

Bring in cookies for the class.

300

What are three different ways to describe a derivative?

slope of a curve at a point, slope of the tangent line at a point, limit of the difference quotient, instantaneous rate of change

300
lim┬(x→2) ⁡3/(4x)
3/8
300

What is the second derivative of the position function?

acceleration

400

If f '' (x) = 12, what can we say about the function?

It is always concave up.

400

The college where Ms. Megs earned her bachelor's degree.

Wellesley College

400
If f(2)=4, can you conclude anything about the limit of f(x) as x approaches 2?
No
400
lim┬(x→3)⁡〖(√(x+1)-2)/(x-3)〗
1/4
400

What is the derivative of f(x) = x3 at x = 1?

3

500

If T=f(t) is a function that tells the temperature, in degrees Celsius, at time after 12 am on a certain day, what are the units of the derivative of the inverse function?

hours after midnight per degree Celsius

500

What were Ms. Meg's two undergraduate degrees in?

Math and Chinese Studies

500

If the limit of f(x) as x approaches 2 is 4, can you conclude anything about f(2)?

No

500
lim┬(x→4)⁡〖(x^2-5x+4)/(x^2-2x-8)〗
1/2
500
If  f '  is greater than zero at x = 2, what can you say about the function f(x) there?

It is increasing (i.e. its slope is positive),