To find the slope of this problem, we should use the slope formula:
m = (y2 - y1)/(x2 - x1)
And then use the following combinations together: 1.1 to 1.2, 1.2 to 1.3 and 1.1 to 1.3 to determine how the slope is around 1.2
m = (f(1.2) - f(1.1))/(1.2 - 1.1)
m = (4.38 - 4.18)/(0.1) = .2/.1 = 2
m = (f(1.3) - f(1.2))/(1.3 - 1.2)
m = (4.56 - 4.38)/(0.1) = .2/.1 = 1.8
m = (f(1.3) - f(1.1))/(1.3 - 1.1)
m = (4.56 - 4.18)/(0.2) = .38/.2 = 1.9
This means the derivative will be between 1.8 < f'(1.2) < 2.0. And that choice would be D.