Name: Introduction to average rate of change | Functions | Algebra I | Khan Academy
Uploaded: 2018-06-18T13:17:43.000Z
Duration: 5 min 31 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

The imperative

and let's say that d is
distance and t is time,

so this is giving us our
distance as a function of time,

and you can see the graph
of how distance is changing

we refer to as the slope of a
line and we can figure it out,

we can figure out, well,
for any change in time,

if we're going from time
equal one to time equal two,

our change in time,
delta t is equal to one

We go from distance is
equal to four meters,

to distance in seven
meters at time equal two

and so our change in distance
here is equal to three

it's three meters for
every one second in time

and so our slope would be
our change in our vertical

which would be change in
d, delta d over delta t,

or we could just write that
as three meters per second

if you're thinking about
your change in distance

over change in time,
this rate right over here

This is all a review of
what you've seen before

or if we're talking
about a linear function,

is that your rate does
not change at any point,

the slope of this line
between any two points

but what's interesting about
this function on the right

our rate of change is constantly changing

and we're going to study
that in a lot more depth,

of a foundational primer
for that future state,

where we learn about differential calculus

is think about the instantaneous
rate of change someplace,

if you ever think about
the slope of a line,

and then over here, it looks
like it's a little bit steeper,

to later think about
instantaneous rate of change,

and the way that we think about
our average rate of change

is we use the same tools, that
we first learned in algebra,

that a secant is something
that intersects a curve

in two points, so let's
say that there's a line,

that intersects at t equals
zero and t equals one

and so let me draw that
line, I'll draw it in orange,

and you could do the
slope of the secant line

well, what is that average
rate of change going to be?

Well, the slope of our
secant line is going to be

our change in distance
divided by our change in time,

so our distance has
increased by one meter,

or we could say that our
average rate of change

over that first second from t equals zero,

Well, once again, we can
look at this secant line

so the slope here,
which you could also use

the rate of change seems
to be constantly changing,

Subtitles ListPlay Video

Introduction to average rate of change | Functions | Algebra I | Khan Academy

constantly

recognize

figure

situation