A town has a population of 4000 and grows at 3.5% every year. To the nearest year, how long will it be until the population will
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First find the critical points of <em>f</em> :
so the point (1, 0) is the only critical point, at which we have
Next check for critical points along the boundary, which can be found by converting to polar coordinates:
Find the critical points of <em>g</em> :
where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at
So <em>f</em> has a minimum of -7 and a maximum of 299.