Given the function( ) ( 3)( 2)y x x x= + − , for4 4x−   . What is the value of x atwhich the function has a minimum?(A)32−(B)12−(C)12(D)32

To find the value of x at which the function has a minimum, we need to find the critical points of the function.

Step 1: Take the derivative of the function with respect to x.

The derivative of (3x^2 - 2x + 4) is 6x - 2.

Step 2: Set the derivative equal to zero and solve for x.

6x - 2 = 0 6x = 2 x = 2/6 x = 1/3

Step 3: Check the second derivative to determine if the critical point is a minimum or maximum.

The second derivative of (3x^2 - 2x + 4) is 6.

Since the second derivative is positive, the critical point x = 1/3 corresponds to a minimum.

Therefore, the value of x at which the function has a minimum is 1/3.

So, the correct answer is (B) 1/3.