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Section Number: ________________________ Date:__________________________________
Math 1 42 Quiz 6 - 2 .6B-3.
Instructions: Use correct notation and show all work to find the correct answers.
“An Aggie does not lie, cheat, or steal or tolerate those who do.” X_____________________
- ( 6 pts) Two airplanes are flying in the air at the same height. Airplane A is flying east at 200
mi/h, and Airplane B is flying north at 25 0 mi/h. They are both headed to the same airport
which is located 4 0 miles east of Airplane A and 3 0 miles north of Airplane B. At what rate
is the distance between the airplanes changing?
- ( 5 pts) Find the critical values of 𝑓(𝑥) if 𝑓(𝑥) = 𝑥
4
5 𝑥
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Section Number: ________________________ Date:__________________________________
Instructions: CLEARLY WRITE EACH CORRECT ANSWER IN THE BLANKS PROVIDED!
- Let 𝑓(𝑥) = √
𝑥 ⋅ ln(𝑥). Find where 𝑓(𝑥) is decreasing.
a) (−∞, 𝑒
− 2
b) ( 0 , ∞) only
c) (𝑒
− 2
, ∞) only
d) ( 0 , 𝑒
− 2
) only
- Let 𝑓′(𝑥) =
( 𝑥− 1
)
2
( 𝑥+ 2
)
3
𝑥
. Find where 𝑓(𝑥) is increasing.
a)
b)
c) (−∞, − 2 ), ( 0 , ∞)
d) (−∞, − 2 ), ( 0 , 1 )
- A rectangle has a length that is decreasing at a rate of 3 cm/s, and its width is increasing at
a rate of 2 cm/s. Find the rate at which the area of the rectangle is changing when the
length is 5 cm and the width is 3 cm.
a) 1 𝑠𝑞 𝑐𝑚/𝑠
b) 6 𝑠𝑞 𝑐𝑚/𝑠
c) 19 𝑠𝑞 𝑐𝑚/𝑠
d) 21 𝑠𝑞 𝑐𝑚/𝑠
3 ) __________________
4 ) __________________
5 ) __________________
