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Evaluate where F(x) is differentiable

by sprite1608
Tags: differentiable, evaluate
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sprite1608
#1
Mar18-12, 05:00 PM
P: 2
Hi there, I cannot seem to figure this question out.

1. The problem statement, all variables and given/known data
Let f: [0,3] -> R be defined as follows
x if 0≤x<1,
f(X)= 1≤x<2
x if 2≤x≤3
obtain formulas for F(x) = for 0≤x≤3 and sketch the graphs of f(x) and F(x). Where is F(x) differentiable? Evaluate F(x) where differentiable.


I missed a day of class and am now totally lost. I've read through the sections in Intro to real analysis by Bartle that cover this section and I get no where. Any help on where to go would be greatly appreciated!
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HallsofIvy
#2
Mar18-12, 06:37 PM
Math
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P: 39,682
Quote Quote by sprite1608 View Post
Hi there, I cannot seem to figure this question out.

1. The problem statement, all variables and given/known data
Let f: [0,3] -> R be defined as follows
x if 0≤x<1,
f(X)= 1≤x<2
You are missing the definition of f(x) for x between 1 and 2.

x if 2≤x≤3
obtain formulas for F(x) = for 0≤x≤3 and sketch the graphs of f(x) and F(x). Where is F(x) differentiable? Evaluate F(x) where differentiable.


I missed a day of class and am now totally lost. I've read through the sections in Intro to real analysis by Bartle that cover this section and I get no where. Any help on where to go would be greatly appreciated!
Hopefully, you know that f(x)= x is differentiable for all x. I suspect that the missing formula for x between 1 and 2 also defines a differentiable function. If that is the case, the only problem is whether the function is differentiable at the "joints", x= 1 and x= 2. Apply the definition of the derivative,
[tex]\lim_{h\to 0}\frac{f(a+h)- f(a)}{h}[/tex]
with a= 1 and then with a= 2. Look at the one sided limits.
sprite1608
#3
Mar18-12, 06:46 PM
P: 2
Quote Quote by HallsofIvy View Post
You are missing the definition of f(x) for x between 1 and 2.
shoot. I missed that when I checked it over. it is f(x) = 1 if 1≤x<2

With that information, would it really make much of a difference to what you said previously?

SammyS
#4
Mar18-12, 08:40 PM
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Evaluate where F(x) is differentiable

Quote Quote by sprite1608 View Post
Hi there, I cannot seem to figure this question out.

1. The problem statement, all variables and given/known data
Let f: [0,3] -> R be defined as follows
x if 0≤x<1,
f(X)= 1 if 1≤x<2
x if 2≤x≤3
obtain formulas for F(x) = for 0≤x≤3 and sketch the graphs of f(x) and F(x). Where is F(x) differentiable? Evaluate F(x) where differentiable.

I missed a day of class and am now totally lost. I've read through the sections in Intro to real analysis by Bartle that cover this section and I get no where. Any help on where to go would be greatly appreciated!
You have f(x) and F(x). What relationship is being assumed between those two functions?


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