Concept explainers
A high-tech company purchases a new computing system whose initial value is V. The system will depreciate at the rate f = f(t) and will accumulate maintenance costs at the rate g = g(t), where t is the time measured in months. The company wants to determine the optimal time to replace the system.
(a) Let
Show that the critical numbers of C occur at the numbers t where C(t) = f(t) + g(t).
(b) Suppose that
and
Determine the length of time T for the total depreciation
(c) Determine the absolute minimum of C on (0, T].
(d) Sketch the graphs of C and f + g in the same
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Calculus: Early Transcendentals
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