Chapter 8 Test Flashcards
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?
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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)
