Name:
AP CALCULUS BC
1. Find all inflection points for ( )
2. Find the maximum value of ( )
on [–2,3].
(Find the y number at the absolute maximum point)
3. Find the absolute minimum value (the y number) of ( )
on [-1,2].
4. Which point on the graph of f(x) is f ' (x) < 0 and f " (x) > 0?
5. The curve of ( )
is concave down on what interval?
6. Find all critical points for ( )
7. On what intervals is ( )
.
increasing?
8. A couple have enough wire to construct 160 ft of fence. They wish to use it to form three sides of a
rectangular garden, one side of which is along a building. Find the dimensions that will yield the largest area.
9. A function ƒ is continuous on the interval [–3, 3] such that ƒ(–3) = 4 and ƒ(3) = 1. The functions ƒ‘ and f ’’
have the properties given in the table below:
x
f ’(x)
f ‘’(x)
–3 < x< –1
Positive
Positive
x = –1
Fails to Exist
Fails to Exist
–1 < x < 1
Negative
Positive
x=1
Zero
Zero
1<x<3
Negative
Negative
a) What are the x–coordinates of all the absolute maximum and absolute minimum points of ƒ on the
interval [–3, 3]? Justify your answer.
b) What are the x–coordinates of all points of inflection of ƒ on the interval [–3, 3]? Justify your answer.
c) Sketch and label a graph that satisfies the given properties of ƒ.
A particle moves along a horizontal line so that its position at any time is given by
( )
, where s is measured in meters and t in seconds.
(a) Find the instantaneous velocity at time t and at t = 4 seconds.
(b) When is the particle at rest? Moving to the right? Moving to the left? Justify your
answers.
(c) Find the displacement of the particle after the first 8 seconds.
(d) Find the total distance traveled by the particle during the first 8 seconds.
(e) Find the acceleration of the particle at time t and at t = 4 seconds.
(f) When is the particle speeding up? Slowing down? Justify your answers.