Question: Plotting smooth curve via PolynomialInterpolation command

Hi

Two sets of ordered pairs (i.e. A and B) are calculated in a problem.

A = {[0.5, 3.15], [1, 4.87], [1.5, 6.56], [2, 8.22]}

B = {[0.5, 3.67], [1, 4.94], [1.5, 5.29], [2, 5.93]}

Two control points are considered to check the validity of interpolated polynomials as follows:

- Control point for A:

  Calculated by interpolation [1.75, 7.3959] ... Exact amount [1.75, 7.3971]

- Control point for B:

  Calculated by interpolation [1.75, 5.4981] ... Exact amount [1.75, 5.6225]

The calculated polynomial via interpolation for sets A and B are plotted for independent variable between 0.5 and  2. The plot of interpolated polynomial for A is a curve without local extremum. However ordered pairs in B show that the polynomial should be a strictly increasing function, but the plot of interpolated polynomial for B has many local extremums. By increasing ordered pairs in B, the local extremums are increased. Moreover, the control point for B shows that the interpolated polynomial is not reliable. 

The more exact ordered pairs for B are presented in below. If more ordered pairs are required for interpolation, you can use them.

{[0.75, 4.1457],[1.25, 4.9448],[1.75,5.62]}

How can I find the best curve fitting for ordered pairs in B?

Thank you for taking your time