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.