AP Calculus 3.7-3.9 Quiz
Name: __________________________________
dy
for the following:
dx
1. 3 cos x  sin y  xy 2
Find
2. ye 3  4x 2 y 5  y  e y

3.
4. y  log 4 (3  5x)
y  x 3e 2 x
6. y  (ln x 2 ) 3
5. y  ln( x 2  5x)

8. y  tan1 ( x )
7. y  cos 1 (3x 2 )

9. y  4 2 x 7
10.

y  x sin x
11. Find an equation of the line that is normal to the curve 4 x  2 x 2 y  y 2  23 at (2,3) . Find the x-coordinate of
each point on the curve where the tangent line is vertical.
12. Find an equation of the lines that are tangent to the curve x 2  2 y 2  9 at x 1. Find all points on the curve
where the tangent line is parallel y 10 .


For #13-17: A particle moves along the x-axis so that at any time t > 0 its position is given by x(t) = t3 – 12t + 5
13. Find the velocity of the particle at any time t.
14. Find the acceleration of the particle at any time t.
15. Find all values of t for which the particle is at rest.
16. Find the speed of the particle when its acceleration is zero.
17. Is the particle moving toward the origin or away from the origin when t = 3? Justify your answer.

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