# Find the Local Minimum

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The profit P(t) for a firm as a function of time (t) is described by the equation

P(t) = t ? 3/8 t^2 + 1/24t^3

For 0 < t =< 10 show that there is exactly one local minimum, and find the value of t at which it occurs. Is the profit positive at this local minimum?

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##### Solution Summary

The local minimum of a function is found. The expert determine if the profit is positive at the local minimum.

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Actually,we rewrite the equation as P(t)=1/24*t*(t^2-9*t+24).And we notice ...

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