AP Calculus
Answers to 6.1 quiz practice sheet
1. S(t) = sin (t) + 2
2. Hint: change (𝑥 + 1)2 to 𝑥 2 + 2𝑥 + 1 before taking the antiderivative, then plug in (-2, 8) as
your “initial condition”.
1
Answer: y = 3 𝑥 3 + 𝑥 2 + 𝑥 +
26
3
3. (we did this in class)
a.
𝑦=
1 2
𝑥
2
+ 𝑥 + 107
b. 419 oz or 26 lb, 3 oz
3. (why did I call this #3? Not sure…) 5 tan(x) + c
4. -.5 csc (2x) + c
5.
6.
2 5𝑥
𝑒 +𝑐
5
4
− 𝑥 − 5 ln(𝑥) +
𝑐
7. Take antiderivative of y’(t) = 802.137𝑒 1.528𝑡 to get: 𝑦 =
initial condition (t=0, y=750) to get: 𝑦 =
802.137 1.528𝑡
𝑒
1.528
802.137 1.528𝑡
𝑒
1.528
+ 𝑐, then plug in
+ 1.42868. Then plug in t=12 to get:
4.823x1010 bacteria.
8-9. I’ll have to show you these answers in class.
10. A (if dy/dx is cos x, then the graph should be showing the shape of the function that has a
derivative of cos x, which is the sin x graph.)
11. B