Test # 3 Review Math MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Test # Review Math Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identif the functionʹs etreme values in the given domain, and sa where the are assumed. Tell which of the etreme values, if an, are absolute. ) g(t) = t - 9 t + 8t, 0 t < ) A) local and absolute minimum: - 0 at = 8; local maimum: B) local minimum: 0 at = 0; local and absolute minimum: - 0 = C) local minimum: D) local minimum: at = at = 8; local maimum: at at =; local maimum: 0 at = 0; absolute maimum: - 0 at = 8 at =; local and absolute maimum: - 0 at = 8 Use lʹhopitalʹs Rule to evaluate the limit ) lim ) A) 8 7 B) C) 8 D) Solve the problem. ) Suppose that c() = is the cost of manufacturing items. Find a production level that will minimize the average cost of making items. A) 9 items B) 7 items C) There is not a production level that will minimize average cost. D) - items ) Find an antiderivative of the given function. ) ) A) 8 B) 8 7 C) - 8 D) 9 Solve the initial value problem. ) d d = -/, () = ) A) = / - B) = / + C) = / - D) =- -7/ -

2 Solve the problem. ) Given the acceleration, initial velocit, and initial position of a bod moving along a coordinate line at time t, find the bodʹs position at time t. a =, v(0) =, s(0) = A) s = t + t + B) s = t + t + C) s = -t - t + D) s = t + t ) Use Newtonʹs method to estimate the requested solution of the equation. Start with given value of 0 and then give as the estimated solution. 7) + + = 0; 0 = -; Find the one real solution. 7) A) -0.9 B) -0. C) -0.8 D) -0. 8) = 0; 0 = 0; Find the left-hand solution. A) 0. B) -0. C) 0. D) 0. 8) Solve the problem. 9) Find the number of units that must be produced and sold in order to ield the maimum profit, given the following equations for revenue and cost: R = C = A) 0 units B) 0 units C) 0 units D) 80 units ) Suppose a business can sell gadgets for p = dollars apiece, and it costs the business c() = 00 + dollars to produce the gadgets. Determine the production level and cost per gadget required to maimize profit. A) gadgets at $8.89 each B),000 gadgets at $0.00 each C),70 gadgets at $.0 each D),0 gadgets at $7.0 each 9) ) ) Find the number of units that must be produced and sold in order to ield the maimum profit, given the following equations for revenue and cost: R() = 0-0. C() = 9 +. A) units B) units C) 9 units D) units ) ) Find the optimum number of batches (to the nearest whole number) of an item that should be produced annuall (in order to minimize cost) if 70,000 units are to be made, it costs $ to store a unit for one ear, and it costs $0 to set up the factor to produce each batch. A) batches B) batches C) batches D) 8 batches ) ) How close does the semicircle = - come to the point (, )? A) = 0. B) =. C) =. D) =.00 ) Use lʹhopitalʹs Rule to evaluate the limit. ) lim A) 9 B) - C) - D) ) Sketch the graph and show all local etrema and inflection points.

3 ) = ) A) Absolute maima: (-, -), (, -) Local minimum: (0, -7) Inflection points: -,,, B) Absolute maima: (-, -), (, -) Local minimum: (0, -7) No inflection points C) Absolute maima: (-, -), (, -) Inflection points: -,,, D) Absolute minima: (-, ), (, ) Local maimum: (0, 7) Inflection point: -, 8 9,, Graph the equation. Include the coordinates of an local and absolute etreme points and inflection points.

4 ) = + cos, 0 π ) - A) local minimum: π, π - local maimum: π, π + inflection points: π, π, π, π -

5 B) local minimum: π, - local maimum: π, inflection point: π, - C) local minimum: (., -0.) local maimum: (0.,.0) inflection points: (0.78, 0.9), (.,.78) -

6 D) no local etrema inflection point: π, π - Graph the rational function. 8 7) = + 9 7) A) B)

7 C) D) ) = ) A) B)

8 C) D) Use the graph of the function f() to locate the local etrema and identif the intervals where the function is concave up and concave down. 9) 9) A) Local minimum at = ; local maimum at = -; concave down on (-, ) B) Local minimum at = ; local maimum at = -; concave up on (-, ) C) Local minimum at = ; local maimum at = -; concave up on (0, ); concave down on (-, 0) D) Local minimum at = ; local maimum at = -; concave down on (0, ); concave up on (-, 0) Find the largest open interval where the function is changing as requested. 0) Decreasing f() = - A) -, B), C) -, D) -, - 0) ) Decreasing f() = - + A) (, ) B) (-, -) C) (-, ) D) (-, ) ) ) Increasing f() = + A) (-, 0) B) (, ) C) (0, ) D) (-, ) ) 8

9 Using the derivative of f() given below, determine the intervals on which f() is increasing or decreasing. ) f () = ( - )( - ) A) Decreasing on (-, ) (, ); increasing on (, ) B) Decreasing on (, ); increasing on (-, ) (, ) C) Decreasing on (-, ); increasing on (, ) D) Decreasing on (-, -) (-, ); increasing on (-, -) ) Identif the functionʹs local and absolute etreme values, if an, saing where the occur. ) f() = A) local maimum at = ; local minimum at = B) local maimum at = - ; local minimum at = - ) C) local maimum at = -; local minimum at = - D) local maimum at = ; local minimum at = ) f() = + + A) absolute maimum: at = - B) relative minimum: at = -; relative maimum: - at = C) absolute minimum: at = - D) no local etrema ) - ) h() = + + A) local minimum at = -; no local maima B) no local etrema C) local minimum at = -; local maimum at = D) local minimum at = -; local maimum at = ) Find the largest open interval where the function is changing as requested. 7) Decreasing f() = - 8 A) (-, 8) B) (-, -8) C) (-8, ) D) (8, ) 7) 9

10 Answer Ke Testname: TEST # REVIEW MATH SUM 0 ) B ) C ) C ) A ) A ) B 7) B 8) C 9) D ) D ) A ) C ) C ) C ) A ) A 7) C 8) C 9) C 0) A ) D ) A ) B ) C ) C ) D 7) A