http://edugen.wiley.com/edugen/courses/crs4196/art/qb/qu/ch0/EAT_1227298660014_0_33367326491234830.gif Thats the graph of f' and assume f is continuous and f(0)=0 Find f(3)

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http://edugen.wiley.com/edugen/courses/crs4196/art/qb/qu/ch0/EAT_1227298660014_0_33367326491234830.gif Thats the graph of f' and assume f is continuous and f(0)=0 Find f(3)

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Well, what does the value of f' tell you about f?
its the derivative?
Sweethert, keep it in chat please. this is for mmonish's question.

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Yes, but what does the derivative tell you? What does it mean to be the derivative?
i have no idea..HELP
What is the derivative of the function f(x) = 5x + 3?
5
slope?
I can't see your graph
Right. The derivative is the slope of the curve at any given x value.
So, if the derivative is a constant, what does that mean about the curve of the original function?
@myinninaya: i don't know y @polpak: the slope is ?
The slope is a constant.
What does the graph of f(x) = 5x+3 look like?
a line
yes
Right, and you can see that if you take the derivative of a line you will get a constant value for the slope. \(y = mx + b \implies y' = m\)
yea
So look at the graph of f'. What is f' from x=0 to x=2?
straight line...so slope is 0
so you see a horizontal line?
yea
No, the value of f' over that interval is constantly 1. f' = 1 on the interval from 0 to 2.
Which means that f must have a constant slope of 1 over that interval.
ok
So if f(0) = 0, what will f(2) be?
1?
No. Imagine a line with a slope of 1, that goes through the origin.
Where will that line cross the x=2 line?
1/2
Each time x increases by 1, the function increases by 1. That's what it means to have a slope of 1. \(\frac{\text{change in f(x)}}{\text{change in x}}\)
= 1
As much as x changes, the function changes.
So if f(0) = 0, f(2) = ?
1/2
\(\frac{\Delta f}{\Delta x} = 1.\) \(\Delta x = 2 \implies \Delta f =?\)
How much did x change from 0 to 2?
2
The function must also have changed by the same amount if the ratio equals 1
So how much does the function change over that same interval?
2?
Yes
2/2 = 1 = the slope.
So now we know f(2). What do we know about the slope over the interval from x=2 to x=3?
its negative?
Negative what specifically?
slope
We have a graph of f'. The value of f' is the slope of f.
What is the value of f' from x=2 to x=3?
-1
What is the slope of f from x=2 to x = 3?
It's not a trick question =)
The value of f' is the slope of f.
-1
Right.
So if the slope of f is -1 from 2 to 3. And the \(\frac{\text{Change of f}}{\text{Change of x}}\) = Slope = -1, What is the change in x? What is the change in f?
1
1 is which?
x
Right. So \[\frac{\text{Change in f}}{\text{Change in x}} = -1\] \[\frac{\text{Change in f}}{1} = -1\] Change in f =?
-1
Right. So f(2) = 2, and from 2 to 3, the slope of f is -1, then the value of f will change by -1, what is f(3)?
-2?
Is any of this making sense?
No f changes by -1. It goes down 1.
f goes down 1 every time x goes up 1. That's what it means to have a -1 slope. Just like having a slope of 1 means that f goes up 1 each time x goes up 1.
-1
So if f(2) = 2, and x goes up 1, what will f do?
f(3)=3
Your answers are all over the place. I'm not sure what is confusing you about what I'm asking, but clearly something is out of sync. Do you understand what I'm saying about slope?
If I have a line g(x) = x. What is the slope?
1
Ok, and what is g(2) and g(4) and g(5)?
2,4,5
Ok. And on the interval from x=2 to x=4, how much does x increase?
2
And g(x) over that interval increases how much?
2?
Yes
Change in g = g(4)-g(2)
just like change in x was 4-2
So as x increases by 1 , g increases by 1. That is what it means to have a slope of 1.
If we have h(x) = 2x, What is the slope?
i hope you know that this is an antiderivative problem
I do.
But there are some small holes in your understanding that make solving these very easy. If I fill the holes you can answer all these in less than a minute.
oh cool
What is the slope of h?
2
So what is h(2), h(4), and h(5)?
4,8,10
So each time x increases by 1, h increases by how much?
2
And what is the derivative of h?
2
So if I tell you that j(0) = 1, and the derivative of j (also called j') = 5, Can you tell me what j(3) =?
(remember that the derivative is the slope)
15
Very nearly.
That would be the correct answer if j(0) = 0
5x+15
But because j(0) = 1, we need to start at one, and add 15 because the change in x is 3 and the slope is 5.
16?
Yes
Now. If I tell you that f(0) = 0 and the derivative ( also called slope, and f') is 1 from 0 to 2, what is f(2) again?
2
And now if we know that f(2) = 2, and f' = -1 from 2 to 3, what is f(3)?
1
Yes!
so thats the answer
Yes
ok dont help me solve this but let me know if i did it correctly
Ok
f(7)
oh pellet my boss is here...ill ttyl..thanks a ton
lol, k. You can repost the answer here and I'll check back
ok thankls

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