Question

100 POINTS

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Answer 1

Local minimums occur when g'(x) = 0 and g"(x) > 0.

Local maximums occur when g'(x) = 0 and g"(x) < 0.

Set g'(x) equal to 0 and solve:

0 = 2x (x − 1)² (x + 1)²

x = 0, 1, or -1

Evaluate g"(x) at each point:

g"(0) = 2

g"(1) = 0

g"(-1) = 0

There is a local minimum at x = 0.

Answer 2

Local minimum at x = 0.

Explanation:

Local minimums occur when g'(x) = 0 and g"(x) > 0.

Local maximums occur when g'(x) = 0 and g"(x) < 0.

Set g'(x) equal to 0 and solve:

0 = 2x (x − 1)² (x + 1)²

x = 0, 1, or -1

Evaluate g"(x) at each point:

g"(0) = 2

g"(1) = 0

g"(-1) = 0

There is a local minimum at x = 0.