How do you know a particle is speeding up or slowing down?

Velocity and acceleration's signs

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1-14 AP Calc AB Review

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Questions 15

Answers

1
When given v(t) and asked to find the derivative, you're looking for
Position s(t)
The slope of the tangent line of s(t)
Acceleration a(t)
v(t) at a certain point
2
What is the FIRST and crucial step to solving a differential equation?
Find the anti-derivative
Use the initial condition
Add a C
Separate the variables
3
Increasing/Decreasing of an f(x) is determined by
First Derivative Test
Limits of f(x) values
Mins and Maxs
Second Derivative Test
4
The fundamental theorem of calculus (FTC) deals with integrals and anti-derivatives.
True
False
5
Find the derivative of the function below.
18x^2 - 9 + C
18x^2 - 9
18x^3 - 9x
6x^2 - 9
6
The slope of the tangent lines along a curve is also known as?
Concavity
The limit
The derivative
Average rate of change
7
Find this anti-derivative.
1/2x^2 - 5x + C
2x - 5 + C
1/3x^3 - 5/2x^2 + 6x
1/3x^3 - 5/2x^2 + 6x + C
8
Speed is expressed as
The opposite of v(t)
When a(t) and v(t) have the same sign
Absolute Value of v(t)
v(t)
9
What is the slope of the secant line known as?
Average rate of change
Instantaneous rate of change
The tangent line
Derivative
10
Proving continuity requires ALL BUT the following
Proving the value exists on the function
It is differentiable
Proving the limit exists
Limit and Value are equivalent
11
Right Reimann sum is an overestimate when f(x) is
Concave Down
Concave Up
Decreasing
Increasing
12
This limit exists
False
True
13
How do you know a particle is speeding up or slowing down?
Critically thinking with the information is the problem
Velocity's sign
Acceleration's sign
Velocity and acceleration's signs
14
Linearization will be an UNDERESTIMATE when f(x) is
Positve
Increasing
Concave Down
Concave up
15
When f'(x) changes from ________ to _________ you have a relative max on f(x)
Positive, Negative
Decreasing, Increasing
Increasing, Decreasing
Negative, Positive

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