anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Well, what does the value of f' tell you about f?
anonymous
  • anonymous
its the derivative?
anonymous
  • anonymous
Sweethert, keep it in chat please. this is for mmonish's question.

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

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