The graph to the right shows the
distance travelled by a car over time.
(a) When is the car moving fastest?
(b) Is the car speeding up or slowing
down on the interval ?
(c) Is the car speeding up or slowing
down on the interval ?
Explain your answers.

The graph of ƒ is shown at
right.
(a) Where is ƒ' positive?
(b) Where is ƒ'' positive?
(c) What are the critical
numbers of ƒ?

The graph of ƒ' is shown at
right.
(a) Where is ƒ increasing?
(b) Where is ƒ concave up?
(c) If ƒ(1) = 0, is ƒ(0)
positive or negative?
Explain.

The graph of a function ƒ with domain [0, 10] is shown in the figure.
Several points are labeled.
(a) List all labeled points at which ƒ'(x) > 0. (b) List all critical points of ƒ.
(c) List all labeled
points at which
ƒ''(x) > 0. H
C G I
B D F J
K
E
A

Willy the Wallaby
Willy the Wallaby and his friends decided to
race each other one afternoon. Willy, being the
super-powered marsupial that he is,
volunteered to race first. His position is
described by the function f(t). Roo, his friend
from school, raced against him, and his red-necked wallaby
position is represented by g(t), the line tangent
to f(t) at t=0. They started at t=0 and raced for
8 seconds. Whoever ran the furthest at the end
of 8 seconds was the winner. Who won the
race and why?
HOMEWORK