Example 1.  Find the cubic Hermite polynomial or "clamped cubic" that satisfies  
          

Solution 1.

Enter the formula for a general cubic equation.

Symbolic differentiation (integration too) is permitted with Mathematica.

Set up four equations using the prescribed endpoint conditions. Then find the solution set to this linear system and store it in the variable solset.

Use the solution given above for the coefficients and form the cubic function.  Remember that we must dig out one set of braces using   before we can use the ReplaceAll command.

(c) John H. Mathews 2004