MATH 140 INSTRUCTIONS You must show all work, and check work. MULTIPLE CHOICE Select the best answer choice. Write your answer choices below: (1) I. _____ II. _____ III. _____ (2) _____ 1) Match each of the following graphs to the appropriate conditions for Explain. I. f' and f '' . y=f ( x ) 0 1 2 II. y=f ( x ) 0 1 2 III. y=f ( x ) 0 1 2 A. ' '' '' f ( x )> 0 on ( 0,2 ) , f ( x ) <0 on ( 0, 1 ) , f x> 0 on (1, 2 ) B. f ' ( x )> 0 on ( 0,1 ) , f ' ( x ) <0 on ( 1, 2 ) , f ' x> 0 on ( 1,2 ) , f ' ' ( x ) <0 on ( 1, 2 ) c. f ' x> 0 on ( 0,1 ) , f ' ( x ) <0 on ( 1, 2 ) , f ' x> 0 on ( 0,2 ) D. ' ' '' f ( x )> 0 on ( 0,1 ) , f ( x ) <0 on ( 1, 2 ) , f ( x )< 0 on ( 0,2 ) E. f ' ( x )< 0 on ( 0,1 ) , f ' ( x ) >0 on ( 1, 2 ) , f ' ' ( x )< 0 on ( 0,1 ) , f ' ' ( x ) >0 on ( 1, 2 ) Write the letter that corresponds to the correct graph: (I) __________ (II) __________ (III) __________ 2) Engineers want to design an auxiliary pipeline from a new natural gas source; 3 km from the main pipeline, to a power plant located 10 km down the main pipeline, in the least amount of time (see Figure 1). If the oil can flow 10 km/hr along the auxiliary pipeline (OB) and 15 km/hr along the main pipeline (AP), where should the engineers join the auxiliary pipeline to the main pipeline to get the gas to P as soon as possible? Figure 1 Nat ural Gas Sou rce O 3 A x 1 0 10 -x P Powe r Plant 5) _____________ (A) 0 (B) 0.89 (C) 0.97 (D) 6/ B 5 (E) None of the above