How do you find horizontal asymptotes?

Find the limit as x→±∞. It is at y = limit

How do you find the zeros of a function?

Graph it and calculate the zeros, Set the function equal to zero

What are critical points of a function?

where f '(x) = 0 or is undefined

Which statement is false?

If f(x)>0, then f'(x) is increasing

You want to find a maximum or a minimum. What is the first step?

Set f ' (x) = 0 (or undefined) to find the critical points

You want to find where the slope of f(x) is increasing. What do you do?

Find the intervals where f "(x) > 0

How do you find the slope of a tangent line at a point?

Plug the x-value into the derivative

How do you find the average rate of change?

find the slope [f(b) - f(a)] / (b - a)

In what form should you write equations?

any form that doesn't require doing any extra work

How do you find vertical asymptotes?

Where the denom=0. If it doesn't simplify, its x=that value

How do you find the slope of a line normal to f(x) at a point.

Plug into the derivative and take the opposite reciprocal

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AP Calculus exam review 1

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AP Calculus exam review questions about limits and derivatives

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Questions 25

Answers

1
How do you find horizontal asymptotes?
Find the limit as x→±∞. It is at y = limit
Where the denom=0. If it doesn't simplify, its y=that value
Where the denom=0. If it doesn't simplify, its x=that value
Find the limit as x→±∞. It is at x = limit
2
If f(x) is increasing, then...
f " (x) is positive
f(x) is positive
f ' (x) is increasing
f ' (x) is positive
3
How do you find the zeros of a function?
Graph it and calculate the zeros
Set the function equal to zero
Graph it and look for horizontal tangents
Take the derivative and set it equal to zero
4
What is the lim x→0 of sin(x)/x
∞
1
0
DNE
5
If f(a)=b and f '(a)=c, then what is the derivative of f ^-1(x) at x = b?
-1/c
-1/a
1/c
1/a
6
What are critical points of a function?
where f '(x) = 0
where f ''(x) = 0
where f(x) = 0
where f '(x) = 0 or is undefined
7
What values should check if you're looking for an absolute max or min?
end points
critical points and end points
critical points
Just graph it and guess
8
Which statement is false?
If f(x)>0, then f'(x) is increasing
If f "(x)<0, then f(x) is concave down
If f '(x) is increasing, then f "(x)>0
If f '(x)>0, then f(x) is increasing
9
If f(x) is decreasing, then...
f (x) is negative
f ' (x) is decreasing
f ' (x) is negative
f " (x) is negative
10
What are inflection points of a function?
where f "(x) changes signs
where f(x) = 0
where f '(x) = 0
where f ''(x) = 0
11
You want to find a maximum or a minimum. What is the first step?
Sketch a graph by hand
Set f '' (x) = 0 (or undefined) to find the critical points
Set f(x) = 0 (or undefined) to find the critical points
Set f ' (x) = 0 (or undefined) to find the critical points
12
If f ' (x) is decreasing, then...
f(x) is negative
f '' (x) is decreasing
f " (x) is negative
f ' (x) is negative
13
You want to find where the slope of f(x) is increasing. What do you do?
Find the intervals where f "(x) > 0
Find the intervals where f '(x) > 0
Find the intervals where f(x) > 0
Sketch a graph by hand
14
If f '' (x) is positive, then...
f(x) is concave up
f(x) is increasing
f(x) is positive
f ' (x) is concave up
15
If given an interval and asked if f(x)=c at any point on the interval, what theorem do you use?
Extreme Value Theorem
Intermediate Value Theorem
Rolle's Theorem
Mean Value Theorem
16
How do you find the slope of a tangent line at a point?
Plug the x-value into the anti-derivative.
Plug the x-value into the second derivative
Plug the x-value into the derivative
Plug the x-value into the function
17
What is the lim x→∞ of sin(x)/x
∞
DNE
0
1
18
How do you find the average rate of change?
find the derivative and plug in
find the slope [f(b) - f(a)] / (b - a)
find the slope [f '(b) - f '(a)] / (b - a)
19
In what form should you write equations?
y = mx + b
any form that doesn't require doing any extra work
20
How do you find vertical asymptotes?
Where the denom=0. If it doesn't simplify, its y=that value
Where the denom=0. If it doesn't simplify, its x=that value
Find the limit as x→±∞. It is at x = limit
Find the limit as x→±∞. It is at y = limit
21
Given f(x), how do you find the slope at x = c?
Make up a number
Plug c into f(x)
Find two points around c and calculate their slope
Plug c into f ' (x)
22
If given an interval & asked if f '(x)=c at any point on the interval, what theorem do you use?
Rolle's Theorem
Mean Value Theorem
Intermediate Value Theorem
Extreme Value Theorem
23
If f '(x) is increasing, then...
f '(x) is positive
f ''(x) is increasing
f(x) is positive
f "(x) is positive
24
How do you find the slope of a line normal to f(x) at a point.
Plug into the derivative and take the reciprocal
Plug into the function and take the opposite reciprocal
Plug into the derivative and take the opposite reciprocal
Plug into the function and take the reciprocal
25
If f '' (x) is negative, then...
f(x) is concave down
f(x) is decreasing
f ' (x) is negative
f ' (x) is concave down

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