Yet another practice M403K 2nd midterm from another instructor:

1) (10 points) How much money should we invest today at a rate of tex2html_wrap_inline21 compounded continuously if we need tex2html_wrap_inline23 in three years time?

2) (10 points) Find the differential of tex2html_wrap_inline25 when x=0 and tex2html_wrap_inline29 .

3) (25 points) Let


be a price-demand equation for a certain product. Find the rate of change of p when tex2html_wrap_inline35 and x is decreasing at a rate of tex2html_wrap_inline39 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:

tex2html_wrap_inline51   tex2html_wrap_inline53    tex2html_wrap_inline55    tex2html_wrap_inline57    tex2html_wrap_inline59      tex2html_wrap_inline61

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

Lorenzo Sadun

Wed Oct 18 14:29:32 CDT 2000