**Unformatted text preview: **Review Questions - Rates of Change Multiple Choice 1. . 3 . .
For the function f(x) = x + 2x, determme the average rate of change of fix} With respect to 2: over the interval 1 53 X S 3. a. —30 c. 2
b. —2 d. 15
For fix) = 5):, determine the average rate of change of ﬁx) with respect to x over the interval 6 S x S 2.
a. —5 C. 12
b. 5 d. 5
1i
For f(x) = x3 + 3):, determine the average rate of change of ﬁx) with respect to x over the interval 2 S x S 4.
a. —40 c. 3 1
b. —-36 d. 36 . . . . 2 .
What IS the best estlmate of the instantaneous rate of change for the function ﬁx) = —4x at the pomt at» a. 4 c. —3
b. 8 d. 3
4
What is the best estimate of the instantaneous rate of change for the function ﬁx) = x at the point (— 2,-— 2)?
a. x c. 1
b. 1 d. 2
2 If a stone is thrown downward with a speed of 15 m/s from a cliff that is 80 m high, its height in metres after 2‘ seconds is MA") = 80 - 15.? - 4.51:2. Find the stone's average rate of change of distance between 0 s and 1 s. a. —34.6 m/s 0. 34.6 m/s
b. 19.9 m/s d. ~19.9 m/s
2:2 —:
An object moves along a straight path and its position 5 (in m) at t seconds is given by 3(3‘) = I 1 . Find the
+ 1 average rate of change of the object after 3 seconds.
a. 59 c. 29 _ m/s —— m/s 4 4
b. 59 d. 29 — m/s ——— m/s 16 16 Short Answer 8. 2
The table below is used to ﬁnd the instantaneous rate of change of f (x) = 36:: - 243: + 4 at the point (1, 16).
Use the table to ﬁnd the best estimate for this value. 10. 11. 12. 13. 14. 15. 2 , . .
For f(x) = :32: + £22: + C, determme the average rate of change of ﬁx) With respect to x over the interval DSxSi The position of a particle is given by the function 3 {3) = -15 — 9.8!. Find the average rate of change in
distance with respect to time over the ﬁrst 8 seconds. 2 .
The position of a particle is given by the function 3 (I) = IUD - 15.? — 4.9! . Estimate the particle’s
instantaneous rate of change of distance at 1 s. The posrtion of a particle is given by s (I) = .t — 4: + 4, where s is measured in metres and t in seconds. Find
the instantaneous rate of change of distance at 2 s. An approximate model for the distance S metres traveled in 1‘ seconds by a skateboard going down a hill is 2
3 = k! , where k is a constant that depends on the slope of the hill. If, for one particular hill, the value of k is
0.1, estimate the instantaneous rate of change of distance with respect to time at 10 seconds. 3 2:31. A particle moves along a straight path and its position s (in cm) at t seconds is given by 51:!) = Estimate the instantaneous rate of change of the particle at 3 seconds? A ﬂying squirrel took off from a branch and landed on the branch of another tree 6 metres lower. Hint: The function aft?) = 4.9:2 models the distance d in metres the squirrel has travelled after exactly t seconds pass. Interval :1: Ed
Average Rate of Change, 1-; __—_
——_
__
-— --
5.995155 _ a) Copy and complete the table.
b) Estimate how fast the squirrel was falling when it reached the second branch. Review Questions - Rates of Change
Answer Section MULTIPLE CHOICE ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS: NP‘SAF‘P’N?“
UUO>O>U SHORT ANSWER 8. ANS:
48 9. ANS:
3a+b 10. ANS:
—9.8 11. ANS:
—24.8 12. ANS:
0 m/s 13. ANS:
2m/s 14. ANS: 17
The particle is moving backwards at —-— cmfs. 361 55:56
- 15. ANS: Ad 21:
- Average Rate of Change, — a:
1
555156 28175 0
5.95156 0-
5.995356 b) 58.75 m/s 5
1 ...

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- Spring '15
- Derivative, instantaneous rate, average rate, Jeff Bova