This preview shows page 1. Sign up to view the full content.
Problem Sheet 3 for 6401
Due Monday 10 Nov 2008, at the Problem Class. You should hand
in solutions to all problems, but only some of them will be marked.
1. For the following functions, ﬁnd the critical values and local ex
trema (maxima or minima). Describe the intervals in which
f
is in
creasing or decreasing and sketch the graph of
f
.
(a)
f
(
x
) =
x
1
/
3
(
x
3
+
x
2

x
);
(b)
f
(
x
) =
x
2
(
x
2

4)
1
/
3
;
(c)
f
(
x
) = (
x
+ 1)
e
x
2

x
.
2.
C
(
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: x ) = 250 + 100 x + 0 . 001 x 3 is the cost function for a certain commodity. (a) Find the cost of producing 100 units; (b) Find the average and marginal cost functions and their values at x = 100; (c) Find the minimum average cost. 3. Find the following indeﬁnite integrals: (a) R e 2 x dx ; (b) R ( x 517 x 3 ) dx ; (c) R cos 3 x sin xdx . 1...
View
Full
Document
This note was uploaded on 03/03/2010 for the course MATH 6401 taught by Professor Parnovski during the Fall '08 term at UCL.
 Fall '08
 parnovski
 Math

Click to edit the document details