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Unformatted text preview: 6. Letf(x) = x3 + xk l on the interval [0,2]. Verify that the function satisﬁes the hypotheses ofthe Mean Value Thcorcm on the given interval. Then ﬁnd all numbers c that satisfy the conclusion oftlie Mean Value
Theorem. («intrier Bonus Given the graph of the ﬁrst derivative f ' of a function f answer the following questions: (4 marks) (a) 011 what intervals is f increasing? (b) At what values ofx docsfliave a
local maximum or a local minimum? t (c)0u what intervals isfconcax'e up? Concave down? (d) What are the coordinates ofthe inflection points off? \i 7‘“ November, 2006 Math 1140  Test#3 (MVT e 3.7) Name
Instructions St.#: [. Answer each question in the space provided. 2, Show all relevant work for full marks. 3. Programmable or graphical calculators are not permitted. ' ' i
4. You have 1 hour 40 minutes to complete the exam. Total marks: 40 5. Circle your last name and check that you have 6 pages and 6 questions. 3x2 30 30(5— 3x2) 1C
forkm. f (x)=(x—2+5)T 1.Given flx)=x2+5 , Sketch the graph of , by ﬁrst ﬁnding: (a) x and yintercepts (b) asymptotes
(c) Intervals of increase or decrease (d) coordinates of local maxima and minima (e) Intervals of concave up or concave down (0 coordinates of points of inﬂection [For full marks sketch a neat graph, clearly labelling all max/min points, inﬂection points, and intercepts on the
graph] (10 marks) i: more space on next page... ' l
 \
\ ./, 70/" 2. Determine the absolute maximum and the absolute minimum value of f(x) = x4 — 32x2 — 7 on the interval
[5,6]. (4 marks) a ‘ /' Z / _
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HELL 3. Raggs Ltd., a clothing ﬁrm, determines that in order to sell x units, the price per suit must be p = 150 — 0.5x.
It also determines that the total cost of producing x suits is given by C(x) = 4000 + 0.25x2. How many suits must
the company produce and sell in order to maximize proﬁt? What is the maximum proﬁt? (7 marks) 4\: 4. A fence must be built in a large ﬁeld to enclose a rectangular area of 15,625 m2. One side oflhe area is
bounded by an existing fence; no fence is needed there, Material for the fence costs $2 per metre fer the two
ends, and $4 per metre for the side opposite the existing fence. Find the cost of the least expensive fence.
(7 marks) ‘ l A I 5. Given the: priceidcmand equation x ﬂp) : 216  2172‘ {:1} Dcicnninc lhc \uluus of!) for which demand is mulustic and Ihosc l‘or which ii is meluslic. {J nmrfcs}
['1] Discuss l1c cl‘l‘ccl un dcmaml and J‘L‘vcnuc it‘pricc is hlt'ft’u.\'t1[hy 10% whcnp FEl. (3 nmrkx‘) It) Discuss the effect on demand and revenue it‘pricc is :Immxcd by 10% whcnp = 39. (3 marks} ...
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 Fall '06
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 Math

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