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