If f(x)=|x²-5x+6|, then f’(x)= 1)2x-5, ifx>3 2)5-2x, if2<x<3 3)5-2x, if0<x<1 4)2x-5, ifx<2

The derivative of the function f(x) = |x² - 5x + 6| is not as straightforward as the options suggest. The derivative of an absolute value function is not defined at the points where the function inside the absolute value is equal to zero.

However, we can find the derivative of the function inside the absolute value, which is x² - 5x + 6. The derivative of this function is 2x - 5.

Now, the derivative of the absolute value function will be (2x - 5) when the function inside the absolute value is greater than 0, and -(2x - 5) = -2x + 5 when the function inside the absolute value is less than 0.

To find out where the function inside the absolute value is greater than or less than 0, we need to solve the equation x² - 5x + 6 = 0. The solutions to this equation are x = 2 and x = 3.

So, the derivative of the function f(x) = |x² - 5x + 6| is:

1. 2x - 5, if x > 3
2. -2x + 5, if 2 < x < 3
3. 2x - 5, if x < 2

Please note that the derivative is not defined at x = 2 and x = 3.