Find the extrema of the function

Question

​Find the extrema of the function  ​

Quizplus · Accepted Answer

Taking the derivative of the function and setting it equal to zero, we get:
11ea8970_69f2_e5d5_861b_fb52bd7c4015_TB1301_11
Simplifying this, we get:
11ea8970_69f2_e5d6_861b_5bd5be435c27_TB1301_11
Therefore, the only critical point is x = -1/2. To determine if this is a maximum or minimum, we can take the second derivative:
11ea8970_69f2_e5d7_861b_71e8c0efa2a3_TB1301_11
Since this is positive for all x, the critical point x = -1/2 corresponds to a minimum. Therefore, the function has a global minimum at x = -1/2, and the answer is choice D.

​Find the Extrema of the Function ​

Find the Extrema of the Function