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Unformatted text preview: Math 16A (LEC 003), Fall 2007.
Nov. 19, 2007. MIDTERM EXAM 2 KEY NAME(print in CAPITAL letters, ﬁrst name ﬁrst): ___________________________________________ __
NAME(sign): _______________________________________________ _
‘ID#: ___________________________________ __ Instructions: Each of the ﬁrst four problems is worth 15 points, while problems 5 and 6 are
each worth 20 points. Read each question carefully and answer it in the space provided. YOU
MUST SHOW ALL YOUR WORK TO RECEIVE FULL CREDIT. Clarity of your solutions
may be a factor in determining credit. Calculators, books or notes are not allowed. Make sure that you have a total of 7 pages (including this one) with 6 problems. Read through
the entire exam before beginning to work. QMAWMH TOTAL 2 1. Compute the derivatives of the following two functions. Do not simplify! (b) y = «a  sin<2x> ah? )(‘VJ' SM (2X) ‘i‘ \] xl CD4 (1x) ' L 3 2. All edges of a cube are expanding (increasing in length) at the same rate. When the volume of the cube is 8 m3, the volume is increasing at the rate of 2 ma/s. Find the rate of the expansion
of the edges at this time. )<
H
p 4 3. Find the equation of the tangent line to the curve x2113 — 2:3 + y2 + 3 = 0 at the point (2, 1).
(You may leave the equation in the point—slope form.) 2x.53+ Xz'gfjpf ~3Xz+2ﬂjf =0 Wang M ><=2) j=b “E0 81‘ oi __ oi :
44.42:}; 42+2d—3r O 5 4. You are standing on top of a 32 ft tall tower. You throw a rock straight down with velocity 16 ft/sec. How fast is the rock traveling in the moment when it hits the ground? Assume the
accelleration of the rock is constantly ~32 ft/secz. I, ’9‘ =—:—‘_'45't1 .— HJt +32 +£ooa—(‘b'cn an often ‘iﬁ = ~32Jc ~45
OUT . Rock Mrs % aawu"
O...— 4e€' mt +31 0 {we — 2 =£Jc~ba+23 t=i (at) ' VbQ/OoHG W:
*$2\{L—’\£ =—_4& (WM) 6 3:2 + 1
(ac — 1)”
(a) Determine the domain of this function. x :75 1L 1 5. Consider the function f = (b) Determine the intervals on which y = f is increasing and the intervals on which it is decreasing. 2X CX— 0L ’ 2 Cx— i) (Xii ’L '2. ><+4  .>< _.
ADM —;————— *ﬁw XL ~ 4!
x952: X‘LYF’i X—W’O 4 (d) SketCh the graph of y = f (x) and determine the range of this function.
Vie/("Lied M3 Mrici(Z X21.
In,th '. ( O) 4D . No )C'N/i'ﬁFCLHS. 7 6. You own a coffee shop and one of the items you sell, by the pound, are coffee beans which
go by the brand name Resurrection. Currently you sell 60 pounds per month of these, for $10
per pound, but you want to increase the number of pounds sold. You are told that every $0.20
decrease in price, down to price 0, will increase the number of pounds sold by 4 pounds. Each montly order of Resurrection has a fee of $160 regardless of its size. Each pound ordered
carries a price of $4.
(a) Determine the monthly demand, cost, and proﬁt functions for Resurrection. d1)z‘m0mol '. /F~,1O 2 0‘: CK—éO} x _. Go 40 4o=__:1_ 4,0 —.—ix—+S
L64 5‘3 4) 20 (x > 20 (b) Determine the marginal proﬁt when 150 pounds are sold. dP z —_L><+9
2;; 40 *~ At x=4§o: 02g: ~4r+5= ~6 (0) Determine the intervals on which the proﬁt increases and decreases. Determine the sales
level of Resurrection which maximizes the proﬁt, and compute the price and the proﬁt at this
sales level. f—N‘ Xi £O$XSZAO Chew 13:0 ‘
vim{'3 x+13=0 * ).
Glitz) vow x=5o ><=10'43=940'>
oLx
ﬁx) me, xeEKO/ﬂol , to P78 0l>< ‘ :eoﬂD SQ
Elia) MM Xe(50/Zeoj)é0f>\. le as“
X=60 WaMM'M/i "HQ 'PWd—J‘l‘, “WM ‘5; 8': Mal 3:“):64‘3'50'150 Wrote” = as (o ...
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 Order theory, Monotonic function, The Rock, ————— *ﬁw XL

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