151)
A released film has a revenue given by R(t) =20t
t2+ 1 , where R(t) is in millions of dollars
and t is the number of weeks after its release. Sketch the graph of this function.
151)
152)
Find the vertical asymptotes of the following function. Do not sketch its graph.
y=x2+ 3x– 1
(2x+ 1)ex
152)
153)
Use your graphing calculator to find the absolute extrema of f(x) =x3– 4x2+ 3x+ 2 on
0, 4 (round answers to 3 decimal places).
153)
154)
Let f(x) =x2
x– 4 .
(a) Determine the intervals on which f is increasing.
(b) Determine the intervals on which f is decreasing.
(c) Based on your answers to parts (a) and (b), find the values of x for which f has relative
maxima.
(d) Based on your answers to parts (a) and (b), find the values of x for which f has relative
minima.
154)
155)
A company owns an apartment building containing 80 units. If the company charges $300
per month rent, then all units can be rented out, and for every increase of $10 per month in
rent, the company will lose one customer. What rent should be charged to maximize
revenue?
155)
156)
If y=x(x–1)3, find the x–values of all inflection points.
156)
157)
Let y=x4– 4x3.
(a) Determine y’ and y”.
(b) Determine intervals on which the function is increasing; determine intervals on which
the function is decreasing.
(c) Determine the coordinates of all relative maximum and relative minimum points.
(d) Determine intervals on which the function is concave up; determine intervals on
which the function is concave down;
(e) Determine the coordinates of all inflection points.
(f) With the aid of the information obtained in parts (a)–(e), give a reasonable sketch of
the curve.
157)
158)
If y=x4+ 4x3– 18x2– 3x+ 4, find the x–values of all inflection points.
158)
36
159)
Let y=2x– 4
x– 1
(a) Determine all x– and y–intercepts.
(b) Determine equations of all vertical asymptotes and non–vertical asymptotes.
(c) Determine y’ and y”.
(d) Determine intervals on which the function is increasing; determine intervals on which
the function is decreasing.
(e) Determine the coordinates of all relative maximum and relative minimum points.
(f) Determine intervals on which the function is concave up; determine intervals on
which the function is concave down.
(g) Determine the coordinates of all inflection points.
(h) With the aid of the information obtained in parts (a) – (g), give a reasonable sketch of
the curve.
159)
160)
The profit equation for a taco stand is given by P(x) = – 0.4x2+ 100x– 100, where x is the
number of tacos sold, and P(x) is the profit in dollars. Use the first–derivative test to find
when relative extrema occur.
160)
161)
It is estimated that under a short–term energy–assistance plan, n million households will
receive direct aid in meeting home–fuel costs after t years, where n= 2t3– 15t2+ 36t, 0 t
3. For what value of t will n be a maximum?
161)
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