stud
bud
Sign up
Log in
Home
Library
Explore
SAT
More
Duplicate of Applications of Derivatives Review Flashcards | StudBud
Explore
/
Duplicate of Applications of Derivatives Review
Duplicate of Applications of Derivatives Review
12 terms
·
StudBud Administration
·
13 plays
A quick review of calculus topics dealing with the applications of the first and second derivative.
Flashcards
12 cards
F
Practice quiz
P
Host live
L
Questions
12
Answers
1
The Second Derivative Test...
Determines the concavity of f(x)
Locates point of inflection on f(x)
Locates critical points on f(x)
Determines if critical points are local extrema on f(x)
2
The function shown here appears to have how many critical points?
3
4
2
5
3
The First Derivative Test...
Determines if critical points are local extrema on f(x)
Determines the increasing and decreasing behavior of f(x)
Locates critical points on f(x)
Locates point of inflection on f(x)
4
Based on the sign chart, which of the following statements is false?
f(x) is concave down on (0,5)
f(x) has two points of inflection
f(x) has three points of inflection
f(x) is concave up on (-∞,-6)
5
The function shown here appears to have how many points of inflection?
4
5
2
3
6
A point of inflection can be found when...
f"(x)=0 or undefined
f"(x) changes signs
f'(x)=0 or undefined
f'(x) changes signs
7
Find the inflection point for the function f(x)=x
4
-x .
x = 0
x = 1
No point of inflection
x = ∛(1/4)
8
Which of the following is NOT a step when completing an optimization problem.
Draw a diagram
Test minimum or maximum value
Check for change
Develop an equation to optimize
9
Find the interval over which the given function is decreasing.
(1, ∞)
(-∞, -2) U (4,∞)
(-2, 4)
(-∞, 1)
10
Given f(x) =x
2
, find the value c on the interval [1, 3] for which the MVT applies.
x = 2
x = 1/2
x = 0
x = 4
11
Based on the sign chart, which of the following statements is false?
f(x) has three critical points
f(x) has two critical points
f(x) has a relative minimum at x=5
f(x) has a relative maximum at x=-6
12
Find the interval over which the given function is concave up.
(-2, 4)
(-∞, 1)
(-∞, -2) U (4,∞)
(1, ∞)
