AP Calculus AB: Chapter 8 Practice Test
This content consists of flashcards focused on interpreting the slope of tangent lines and the behavior of derivatives at specific points labeled on a graph of a function. It prompts identifying where the slope is zero, where the derivative does not exist, and where the slope is positive.
Below is a graph on which four points have been labeled. At which of the points is the slope of the tangent line zero?
Point B
Key Terms
Below is a graph on which four points have been labeled. At which of the points is the slope of the tangent line zero?
Point B
Below is the graph of a function on which four points have been labeled. Which of the following statements about these points is true?
The derivative of the function at point B does not exist
Below is a graph on which four points have been labeled. At which of the points is the slope of the tangent line positive?
Point D
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 1
1 3
2 -1...
The function f(x)= 4x^3 + 6x^2 + 3x − 2 has a critical point at x = −1/2.Which sign chart describes this critical point?
-
What are the critical points of the function
f (x) = −2x^ 3 + 3x^ 2 + 36x − 68?
x = −2, 3
Related Flashcard Decks
Study Tips
- Press F to enter focus mode for distraction-free studying
- Review cards regularly to improve retention
- Try to recall the answer before flipping the card
- Share this deck with friends to study together
| Term | Definition |
|---|---|
Below is a graph on which four points have been labeled. At which of the points is the slope of the tangent line zero? | Point B |
Below is the graph of a function on which four points have been labeled. Which of the following statements about these points is true? | The derivative of the function at point B does not exist |
Below is a graph on which four points have been labeled. At which of the points is the slope of the tangent line positive? | Point D |
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 1 1 3 2 -1 -1 3 -2 -1 |
The function f(x)= 4x^3 + 6x^2 + 3x − 2 has a critical point at x = −1/2.Which sign chart describes this critical point? | - |
What are the critical points of the function f (x) = −2x^ 3 + 3x^ 2 + 36x − 68? | x = −2, 3 |
What is the minimum value that f (x) = 5x^ 2 + 10x − 4 attains? | -9 |
What is the x value at the maximum of f (x) = (1 − x)^1/3? | This function has no maximum |
How many points of inflection are there for the graph of f(x) = x + 4/x? | 0 |
On which of the following intervals is the graph of f(x) = 6/x^2 + 3 concave up? | (−∞,−1) and (1,∞) |
What are the x-coordinates of the points of inflection of f(x) = x^4 − 4x^3? | x=0 and x=2 |
If the graph of the second derivative of f(x) is shown, on which of the following intervals is f(x) concave up? | (q,s) |
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, on which intervals would f (x) be concave up? | (p, q) |
The graph of f (x), which contains the point (1, 0), is shown. Which of the following statements about f (x) is true? | f ″(1) < f (1) < f ′(1) |
On which interval is f (x) = x^ 3 − 3x ^2 − 9x + 1 increasing? | (−∞,−1) and (3,∞) |
Which of the following equations could be an equation of a vertical asymptote of y=x^2−2x / x^2−6x+8? | x=4 |
Which of the following equations could be an equation of a vertical asymptote of y = x^2−9/x^2+9? | There is no vertical asymptote |
Which equation is represented by the following graph? | y = 2x^2+1 / x^2−x |
Which of the following represents the graph of y = 1−x^2 / x^2−1? | The graph of y = (1 - x²) / (x² - 1) is the line y = -1 with vertical asymptotes at x = ±1. |