Answer:
Therefore, the statement "f(x) has a minimum at the turning point" is true.
Explanation:
The correct statement is:
O e. f(x) has a minimum at the turning point.
To determine the nature of the turning point at x = 2, we can analyze the behavior of the function f(x) = (2x + 1)(x - 2)² in the vicinity of x = 2.
When a quadratic factor (x - 2)² is multiplied by a linear factor (2x + 1), the turning point occurs at the value of x that makes the linear factor equal to zero. In this case, when 2x + 1 = 0, we find x = -1/2. This is the x-coordinate of the turning point.
Now, we need to determine whether the turning point is a minimum or maximum. To do this, we can examine the behavior of the quadratic factor (x - 2)².
Since (x - 2)² is squared, it is always non-negative or zero. When x = 2, the quadratic factor is equal to zero, indicating that the turning point is located at the minimum of the function. Therefore, the statement "f(x) has a minimum at the turning point" is true.