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[answered] 1) Match each of the following graphs to the appropriate co

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1) Match each of the following graphs to the appropriate conditions for

Select for each case and explain.

I. 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 ( 0,1 ) , f ' ( x ) <0 on ( 1, 2 ) , f ' ' ( x )< 0 on ( 0,2 ) B. f ' ( x )> 0 on ( 0,2 ) , f ' ' ( x ) <0 on ( 0, 1 ) , f '' ( x )> 0 on (1, 2 ) C. '

'

''

''

f ( x )> 0 on ( 0,1 ) , f ( x ) <0 on ( 1, 2 ) , f ( x )> 0 on ( 1,2 ) , f ( x ) <0 on ( 1, 2 ) D. '

'

''

f ( x )> 0 on ( 0,1 ) , f ( x ) <0 on ( 1, 2 ) , f ( x )> 0 on ( 0,2 ) f' and f '' . 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) ________

2) (II) _______ (III) ________ Find the length of the shortest ladder that will reach over an 8-ft. high fence to a

large wall which is 3 ft. behind the fence. (See diagram.) Round the result to one

decimal place. (A) 6.3

(B) 8.8

(C) 5.8

(D) 17.6

(E) None of the above 3) 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?

Nat

ural

Gas

Sou

rce O Figure 1 3

A

x (A) 0 B

1

0 10

?x P Powe

r

Plant (B) 0.89

(C) 6/ ?5 (D) 0.97

(E) None of the above 4) Find a value for p so lim e x? 0 2 px ?2 px?1

=6

2

3x (Hint: Use de L?Hopital rule)

(A) 1, (B) 2, (C) 3, (D) 4, (E) Not determined (not existent)

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