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## Homework Statement

f:[1,+∞[→ℝ

x→sqrt(x+2)-sqrt(x-1)

## Homework Equations

show that f([1,+∞[)=]0,sqrt(3)]

## The Attempt at a Solution

Any tips on how to start it.

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- Thread starter mtayab1994
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- #1

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f:[1,+∞[→ℝ

x→sqrt(x+2)-sqrt(x-1)

show that f([1,+∞[)=]0,sqrt(3)]

Any tips on how to start it.

Last edited:

- #2

Ray Vickson

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Homework Helper

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## Homework Statement

f:[1,+∞[→ℝ

x→sqrt(x+2)-sqrt(x-1)

## Homework Equations

show that f([1,+∞[)=]0,sqrt(3))

## The Attempt at a Solution

Any tips on how to start it.

What have you done so far?

RGV

- #3

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well nothing really, i want something that'll help me get going.What have you done so far?

RGV

- #4

Deveno

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1. calculate f(x) explicitly for a few values of x. i always like 0,1,-1 and 42 (ok, 0,1 and-1 won't work. pick something else. maybe 2,4 and 6)

2. see if lim x→∞ and lim x→1+ exist.

3. see if f(x) has a global maximum or minimum (yeah, derivatives, we can use them, right?)

- #5

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1. calculate f(x) explicitly for a few values of x. i always like 0,1,-1 and 42 (ok, 0,1 and-1 won't work. pick something else. maybe 2,4 and 6)

2. see if lim x→∞ and lim x→1+ exist.

3. see if f(x) has a global maximum or minimum (yeah, derivatives, we can use them, right?)

alright so these 3 steps should help me?

- #6

Deveno

Science Advisor

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you want to figure out how f(x) behaves. you need to get some information.

- #7

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yea but in class when we want to solve something like this he have to show that f(x)=y or f(x)≥0.

- #8

Deveno

Science Advisor

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we need to establish "some" things about f. it's going to be impossible to do, if all you think is "well, f is a function".

take it's derivative. it is always positive, does it ever equal 0, is it some places positive, and some places negative? what does that tell you about f?

are there any places where f(x) = 0 (does this have anything to do with whether or not f crosses the x-axis)?

what happens when x gets "really really big"? does it have a limit as x→∞? if so, what is this limit?

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