Exercise Five: Solution (Calculus)

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

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)


for(S is increasing to the right of 1)

Thus x = 1 corresponds to a minimum.

Find S.

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

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

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