**Exercise
Two: Solution (Algebraic)**

**Problem:**

Find the value of x for which M is a minimum. Also find that minimum
value.

**Solution:**

Recognize that M is a quadratic function of x and that the graph of
the relationship

between x and M is a parabola. The minimum will therefore occur
at the vertex.

The x coordinate of the vertex is given by

Then

Answer:

M has a minimum value of –52 when x is 8.

**Can
you graph the curve M vs. x to confirm the answer? (Graphing
Tool) **

Solution (calculus)

Exercise
One
Exercise
Three