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Unformatted text preview: Math 285
Final Exam, December 16, 2004 Name: SUID No.: CIRCLE your Instructors Name: Dickerson Lindberg Struble Zvoma PLEASE READ: 1. Place all your work on these sheets. Do not add any sheets to this exam. 2. You may use a Tl83 on this exam. You may NOT use any other calculator nor
may you use another student’s calculator. 3. Answers without supporting work/reasons will receive no credit. Label
answers and give units when appropriate. °‘ 4. There are 10 problems (with parts) and 10 pages to this exam including this cover
page and a, blank page for scratch work. Be sure that you have all pages — check
NOW! PLEASE DO NOT WRITE BELOW [\D 10. Total NAME .......................................................... .. 1. A bank offers an account that pays 2.25% interest per year‘ compounded continuously.
A customer puts $2500.00 in the account. °‘ How much will be in the customer‘s acctount after 2 years? Give answer to t1
cent. 1e nearest (b). How long will it take for the customer‘s account to triple? Give answer to the nearest
tenth of a year. 2. Sales (in of CD'S on day 36 of the year is given by: 5(22) 2 1000 + 155 sin(3—76T5:c —10). (a). Find the period, amplitude, vertical shift (that is: midline) of 5(1). (b). Find the sales on day 180. NAME .......................................................... ..
3. The graph of the function f(;r) is pictured below. (21). Using the above picture, ﬁnd the following limits (if a limit does not exist, then write DNEl
[linlL = flzL‘) :
£1131 = fir) : (b). Circle the points where f(3:) is continuous: 1 O 1 [\D (c). Circle the points where is differentiable: 1 0 1 2. NAME .......................................................... .. 4. For the following fuctions, ﬁnd the indicated derivative (do not simplify) (a). f(x) : 1:2 — $151 + ln(;r2) + 6353—2? f/(l‘) :. (b). Mm) : «$3 — tan(2:c), h’(x) :
(C). 10(2) 2 u/(z) : NAME .......................................................... ..
(d). 5(t) : (:os(t3 + 2t2 +12) s”(t) 2. 5. The position (in meters) of a particle moving along a line is given by:
s(t) = t3 + 3252 +16, where t is in minutes. (a). Find the velocity when t : 3.5 minutes. Give units for answer. (b). Find the acceleration when t = 1.5 minutes. Give units for answer. NAME .......................................................... .. 6. A rocket. is rising vertically from its launch pad. An observer is positioned 3,000 feet
from the launch pad. Find the rate of change of the distancewfrom the observer to the
rocket at the moment the rocket is 4,000 feet above the launch pad and is rising at a rate
of 880 feet per second. Make a sketch/identify your variables on the sketch. 0 NAME .......................................................... ..
7. Suppose that 2 $3 + 3:1:2 — 91L“ — 10. Show your work! (a). Find the crtical numbers of Then test each critcal number for a relative max/min
or neither. (b). Find the open intervals on which f(a:) is increasing, and the open intervals on which is decreasing. (c). Find the open intervals on which the graph of is concave up, and the open
intervals on which the graph of f(:r) is concave down. (d). Find the inﬂection point(s) on the graph of f(;r). (This problem is continued on the next page.) 7 NAME .......................................................... .. Make a sketch of the graph of on the coordinate system below. Label and give
the coordinates of the points Where the tangent line is horizontal. and the same for the
inﬂection points. V y 8. 260 feet of fencing is available to enclose and subdivide a rectangular plot of land. The
enclosure is to be subdivided into four parts of equal area (see diagram below). Find the
overall dimensions that will maximize the area of the enclosed plot of land. Show your
work and justify that your dimensions maximize the area. 00 NAME .......................................................... .. 9. Suppose that 1' and y are related by the equation my + $2 — y : 5. (a). Usmg implimt differentiation7 find 1‘. (b). Find an equation of the tangent line to the graph of guy + $2 — y2 = 4 at the point
(2,2). 1.3 y2
10. Suppose that f(:zt,y) = ~3— + 7 — say. (21). Find all the critical points of f(.r, y). (b). Classify (relative max/min or saddle point) the critical points found in part (a). NAME .......................................................... ..
(This page is for scratch work.)  The end 
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