B y 8 x sin x y 8 x sin x y 8 x cos x sin x 1 at 4 π

y = 8 x sin
y = 8 x sin x y' = 8 ( x cos x + sin x
·
1). At , 4
π
,
π
2
y' = 8 cos + sin = 8 (0 + 1) = 8 ,
x
π
2
π
2
π
2
π
2
assignment #7 ...
(b)
3 of 13 9/17/14, 7:42 PM

7. 2/2 points | Previous Answers SCalcET7 3.3.032.
Suppose and let and Find the following.
(a)
(b)
Solution or Explanation
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f (
π
/3) = 3 and f ' (
π
/3) = − 7 , g ( x ) = f ( x ) sin x h ( x ) = (cos x )/ f ( x ).
g' (
π
/3)
h' (
π
/3)
assignment #7 ...
4 of 13 9/17/14, 7:42 PM

8. 6/6 points | Previous Answers SCalcET7 3.3.036.
An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released,
it vibrates vertically. The equation of motion is where s is measured in centimeters and t in seconds. (Take the
positive direction to be downward.)
(a) Find the velocity and acceleration at time t
(b) Graph the velocity and acceleration functions.
(c) When does the mass pass through the equilibrium position for the first time? (Round your answer to two decimal places.)
s = 4 cos t + 8 sin t ,
v ( t ) =
a ( t ) =
.
s
t ≥ 0,
assignment #7 ...
(d) How far from its equilibrium position does the mass travel? (Round your answer to two decimal places.)
(e) When is the speed greatest? (Use n , a positive integer.)
π
π
Solution or Explanation
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3.79 + 3 n
π
5 of 13 9/17/14, 7:42 PM

9. 1/1 points | Previous Answers SCalcET7 3.3.506.XP.
Differentiate the following function.
y' =
Solution or Explanation
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