Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave up
and concave down.
-
A) Local maximum at $x = 1$; local minimum at $x = - 1$; concave up on $( 0 , \infty )$; concave down on $( - \infty , 0 )$
B) Local minimum at $x = 1$; local maximum at $x = - 1$; concave down on $( 0 , \infty )$; concave up on $( - \infty , 0 )$
C) Local minimum at $x = 1$; local maximum at $x = - 1$; concave up on $( 0 , \infty )$; concave down on $( - \infty , 0 )$
D) Local maximum at $x = 1$; local minimum at $x = - 1$; concave up on $( - \infty , \infty )$

Question

Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave up
and concave down.
-
A) Local maximum at $x = 1$; local minimum at $x = - 1$; concave up on $( 0 , \infty )$; concave down on $( - \infty , 0 )$ 
B) Local minimum at $x = 1$; local maximum at $x = - 1$; concave down on $( 0 , \infty )$; concave up on $( - \infty , 0 )$ 
C) Local minimum at $x = 1$; local maximum at $x = - 1$; concave up on $( 0 , \infty )$; concave down on $( - \infty , 0 )$ 
D) Local maximum at $x = 1$; local minimum at $x = - 1$; concave up on $( - \infty , \infty )$

Quizplus · Accepted Answer

- Local minimum at x = 1: The point where the graph changes from decreasing to increasing. 
- Local maximum at x = -1: The point where the graph changes from increasing to decreasing.
- Concave up on (0,∞): The graph is curving upwards, meaning the rate of change is increasing.
- Concave down on (-∞,0): The graph is curving downwards, meaning the rate of change is decreasing.

Use the Graph of the Function F(x) to Locate the Local