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
H
ƒ''(x) > 0.
C G I
B D J
F
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?

What is a limit? Let's look at some functions ...

What is a limit? Let's look at some functions ...

What is a limit? Let's look at some functions ...

What is a limit? Let's look at some functions ...

Source Limit Theorems from Visual Calculus

What is a limit? Let's look at some graphs ...
Source: Practice Quiz on Limits and Graphs
... and some limits:

Let's explore a more symbolic approach ...

WOO!