**Exercise
Five: Solution (Calculus)**

**Problem:**

Find the positive value of
x for which S is a minimum. What is the corresponding minimum value?

**Solution:**

Take
the derivative of S with respect to x.

Set the derivative equal to zero and solve for x.

Since x must positive, disregard the solution x = –1.

Note that

for(S
is decreasing to the left of 1)

and

for(S
is increasing to the right of 1)

Thus
x = 1 corresponds to a minimum.

Find
S.

**Answer:**

S has a minimum value of 2 when x is 1.

**At
x=-1, what can you say about S?**

Exercise
Four
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