Suppose that 4 ≤ f ′(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of f(6) − f(3)? ≤ f(6) − f(3)

The given inequality states that the derivative of the function f(x), f'(x), is between 4 and 5 for all values of x. This means that the slope of the function is between 4 and 5 at every point.

The difference f(6) - f(3) represents the change in the function over the interval from x = 3 to x = 6. This is a difference of 3 units in x.

The minimum possible value of this difference occurs when the slope of the function is at its minimum, which is 4. Over a difference of 3 units in x, the function could increase by 4 * 3 = 12 units.

The maximum possible value of this difference occurs when the slope of the function is at its maximum, which is 5. Over a difference of 3 units in x,