Final answer:
To find the turning point of the function F(x) = (x-1)(x-3)^2(x-1)^2, we can calculate the x-coordinate and y-coordinate of the turning point, determine whether it is a minimum or maximum, and find the coordinates (x, y) of the turning point.
Step-by-step explanation:
To find the turning point of the function F(x) = (x-1)(x-3)^2(x-1)^2, we need to calculate the x-coordinate and y-coordinate of the turning point.
Option 1: To calculate the x-coordinate of the turning point, we need to find the value of x where the first derivative of the function equals zero. This will give us the critical point. We can then substitute this x-value into the original function to find the y-coordinate of the turning point.
Option 2: To calculate the y-coordinate of the turning point, we need to substitute the x-coordinate found in Option 1 into the original function.
Option 3: To determine whether the turning point is a minimum or maximum, we need to analyze the second derivative of the function. If the second derivative is positive, the turning point is a minimum, and if the second derivative is negative, the turning point is a maximum.
Option 4: To find the coordinates (x, y) of the turning point, we can combine the results from Option 1 and Option 2.