Chapter 8 Practice Test Flashcards
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)
