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?

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