Use the graph of the function f(x) to locate the local extrema and identify the

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 minimum at x = 1; local maximum at x = -1; concave up on (- infinity, infinity) B) Local minimum at x = 1; local maximum at x = -1; concave down on (- infinity, infinity) C) Local minimum at x = 1; local maximum at x = -1; concave up on (0, infinity); concave down on (- infinity, 0) D) Local minimum at x = 1; local maximum at x = -1; concave down on (0, infinity); concave up on (- infinity, 0)

Explanation / Answer

C is clearly the correct option since at x =1 the function have a minimum value between -1 and 1, so it is a local minimum.Similarly, at x= -1 function have local maximum.

Function is concave up on (0, infinity) and concave down on (-infinity, 0).

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