**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