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Intro to Calc--Curve Sketching Flashcards | StudBud

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Intro to Calc--Curve Sketching

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Test your knowledge on derivatives and the different ways they can be applied to calculus

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Questions 10

Answers

1
Identify the increasing and decreasing intervals.
Increasing on the entire domain
Inc (∞, 2) and Dec (2, -∞)
Dec (-∞, -2) and Inc (-2, ∞)
Inc (-∞, -2) and Dec (-2, ∞)
2
Relative Extrema
1
4
1/2
2
3
Find the increasing and decreasing intervals...
Increasing: (-3,-1),(2,-∞) Decreasing: (-∞,-3),(-1,2)
Increasing: (-3,-1),(2,-∞) Decreasing: (-∞,3),(1,2)
Increasing: (-3,0),(2,-∞) Decreasing: (-∞,-3),(2,-1)
Increasing: (0,-1),(2,-∞) Decreasing: (-∞,-3),(-2,2)
4
Find the horizontal asymptote of
There isn't any horizontal asymptote
y=0
y=5/2
y=-5
5
For the first derivative test, one must check points that are
Before and after every point of inflection
At every critical value
Before and after every critical value
At every point of inflection
6
Concavity Problem
D
B
A
C
7
Points of inflection are…
Where the concavity changes on f’(x)
Where the second derivative= 0
Where the first derivative= 0
Where the concavity changes on f(x)
8
How many points of inflection are on this graph?
0
2
1
3
9
Find the vertical asymptotes and holes.
Vertical Asymptote: x = 3, Holes: x = 2
Vertical Asymptote: x = -6, x = 1, Holes: none
Vertical Asymptote: x = -3, Holes: x = -2
Vertical Asymptote: x = 2, x = 3, Holes: none
10
If the slope of f(x) is always positive, the function is
Always zero
Both increasing and decreasing at points
Always increasing
Always decreasing