Does the cubic Hermite spline interpolation of a monotone data with known slopes guarantee the monotonicity in interpolation segments?

I am trying to interpolate monotone data with known data values and also known first derivative values at knots. If I used these values with cubic Hermite spline interpolation, Can I guarantee the monotonicity of the interpolation segments?

• Cannot answer, depends on the given slopes. – Yves Daoust Jan 17 at 10:18
• As noted, the condition of being $C^2$ forces you to sacrifice monotonicity in your cubic spline. That being said, there are $C^2$ rational interpolants that also possess monotonicity. You might try researching about them if this is of interest. – J. M. isn't a mathematician Mar 30 at 12:50