Math 1140 Test#3

# Math 1140 Test#3 - 6 Letf(x = x3 xk l on the interval[0,2...

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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 y-intercepts (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 / _ ,‘V K .. lat 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 l|1c cl‘l‘ccl un dcmaml and J‘L‘vcnuc it‘pricc is hlt'ft’u.\'t1[hy 10% whcnp FE-l. (3 nmrkx‘) It) Discuss the effect on demand and revenue it‘pricc is :Im-mxcd by 10% whcnp = 39. (3 marks} ...
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Math 1140 Test#3 - 6 Letf(x = x3 xk l on the interval[0,2...

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