AP Calculus AB: Chapter 8 Test
This set of flashcards explores key concepts in calculus and function analysis, including identifying where tangent lines do not exist, determining intervals with negative derivatives, analyzing slopes of tangents, recognizing symmetry in functions, and finding critical points along with their nature (maxima, minima, or neither). It also covers evaluating maximum values of functions and interpreting sign charts for critical points.
Below is a graph on which four points have been labeled. At which of the points does the tangent line not exist?
Point B
Key Terms
Below is a graph on which four points have been labeled. At which of the points does the tangent line not exist?
Point B
Below is a graph which has been divided into four sections. In which of these sections is the derivative of the function always negative?
Section D
Below is a graph on which four points have been labeled. At which of them is the slope of the tangent line negative?
Point C
Below are four tables with points from y = f (x) listed. Which of the tables could belong to a function that is symmetric around the y-axis?
x y
0 -2
1 14
2 -2...
The function f (x) = 2x^ 3 − 21x ^2 + 72x − 49 has critical points at x = 3 and x = 4. Which sign chart describes these critical points?
The sign chart for f(x)=2x3−21x2+72x−49f(x) = 2x^3 - 21x^2 + 72x - 49f(x)=2x3−21x2+72x−49 shows the derivative changes from positive to negative at...
What are the critical points of the function f(x) = x+1/x?
x = −1, 1
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| Term | Definition |
|---|---|
Below is a graph on which four points have been labeled. At which of the points does the tangent line not exist? | Point B |
Below is a graph which has been divided into four sections. In which of these sections is the derivative of the function always negative? | Section D |
Below is a graph on which four points have been labeled. At which of them is the slope of the tangent line negative? | Point C |
Below are four tables with points from y = f (x) listed. Which of the tables could belong to a function that is symmetric around the y-axis? | x y 0 -2 1 14 2 -2 -1 14 -2 -2 |
The function f (x) = 2x^ 3 − 21x ^2 + 72x − 49 has critical points at x = 3 and x = 4. Which sign chart describes these critical points? | The sign chart for f(x)=2x3−21x2+72x−49f(x) = 2x^3 - 21x^2 + 72x - 49f(x)=2x3−21x2+72x−49 shows the derivative changes from positive to negative at x=3x=3x=3 (local max) and from negative to positive at x=4x=4x=4 (local min). |
What are the critical points of the function f(x) = x+1/x? | x = −1, 1 |
What is the maximum value that f (x) = x^ 3 − 3x ^2 + 3x + 9 attains? | This function has no maximum. |
The function f (x) = x^ 3 − 6x ^2 + 12x + 10 has a critical point that is neither a maximum nor a minimum. What are its coordinates? | (2, 18) |
How many points of inflection are there for the graph of f(x)= −3x^5+5x^3? | 3 |
On which of the following intervals is the graph of f(x) = x^2+1/x^2−4 concave down? | (−2,2) |
What are the x-coordinates of the points of inflection of f(x)=x(x−4)^3? | x=2 and x=4 |
If the graph of the second derivative is shown, on which of the following intervals is f(x) concave down? | (s, t) |
The graph of f(x) is shown. Which of the following intervals has both f′(x)>0 and f′′(x)<0 ? | (q, r) |
If the graph of the derivative of f (x) is shown, at which x-coordinates would f (x) have a point of inflection? | x = q only |
If the graph of the derivative of f (x) is shown, on which intervals would f (x) be concave down? | (q, r) |
On which interval is f (x) = 3x^ 5 − 20x ^3 increasing? | (−∞,−2) and (2, ∞) |
Which of the following equations could be an equation of a vertical asymptote of y=x^2+2x−3/√x | x=0 |
Which of the following equations has no vertical asymptote? | x/x^2 + 2x+ 7 |
Which equation is represented by the following graph? | y=(x+1)^2/x |
Which of the following represents the graph of y=2x−1/x+1? | The graph of y = (2x - 1) / (x + 1) has a vertical asymptote at x = -1, a horizontal asymptote at y = 2, and intercepts at (0, -1) and (0.5, 0). |