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Yet another practice M403K 2nd midterm from another instructor:

1) (10 points) How much money should we invest today at a rate of
compounded continuously if we need
in three years time?

2) (10 points) Find the differential of
when *x*=0 and
.

3) (25 points) Let

be a price-demand equation for a certain product. Find the rate of change
of *p* when
and *x* is decreasing at a rate of
per month. Is the price increasing or decreasing?

4) (55 points) Let

We want to find the absolute maximum of *f*(*x*) on its domain.
For doing that, complete the following steps.

a) (5 points) Find the domain of *f*.

b) (5 points) Find all intercepts.

c) (10 points) Find horizontal and vertical asymptotes, if any.

d) (20 points) Find the intervals where *f* is increasing and those
where it is decreasing. Identify all local maxima and all local minima,
if any.

e) (10 points) Graph *y*=*f*(*x*). You may need some
of the following:

f) (5 points) Identify the absolute maximum and the absolute minimum,
if they exist.

*Lorenzo Sadun*

*Wed Oct 18 14:29:32 CDT 2000*