Determining if an equation has a solution by using the intermediate value theorem

abel muroi

Junior Member
Joined
Jan 13, 2015
Messages
210
Use the intermediate value theorem to determine whether the following equation has a solution or not

SquareRoot(2x) + SquareRoot(1 + x) = 4



I don't understand the formal definition of the intermediate value theorem. Can someone explain it to me in simpler terms?

What am i supposed to do here?
 
Use the intermediate value theorem to determine whether the following equation has a solution or not
.SquareRoot(2x) + SquareRoot(1 + x) = 4
I don't understand the formal definition of the intermediate value theorem. Can someone explain it to me in simpler terms?
That theorem states that there are no gaps in the graph of a continuous function.
If f(x)=2x+1+x\displaystyle f(x)=\sqrt{2x}+\sqrt{1+x} then f(x)\displaystyle f(x) is continuous.
f(0)<4<f(8)\displaystyle f(0)<4<f(8)
 
Use the Intermediate Value Theorem to determine whether or not the following equation has a solution:

. . . . .\(\displaystyle \sqrt{\strut 2x\,}\, +\, \sqrt{\strut 1\, +\, x\,}\, =\, 4\)

I don't understand the formal definition of the intermediate value theorem. Can someone explain it to me in simpler terms?

What am i supposed to do here?
What is the full and exact text of your book's statement of the Intermediate Value Theorem? Thank you! ;)
 
What is the full and exact text of your book's statement of the Intermediate Value Theorem? Thank you! ;)

And I want to add to it:

Exactly where in that statement you get lost...
 
Use the intermediate value theorem to determine whether the following equation has a solution or not
SquareRoot(2x) + SquareRoot(1 + x) = 4
I don't understand the formal definition of the intermediate value theorem. Can someone explain it to me in simpler terms?
And I want to add to it:
Exactly where in that statement you get lost...
As long as we are concerned statements, theorems do not have definitions. They have proofs.

If f\displaystyle f is continuous and L\displaystyle L is between f(a) & f(b)\displaystyle f(a)~\&~f(b) then there is a t between a & b\displaystyle t\text{ between }a~\&~b such that f(t)=L\displaystyle f(t)=L.
That is the statement of the intermediate value theorem.
 
As long as we are concerned statements, theorems do not have definitions. They have proofs.

If f\displaystyle f is continuous and L\displaystyle L is between f(a) & f(b)\displaystyle f(a)~\&~f(b) then there is a t between a & b\displaystyle t\text{ between }a~\&~b such that f(t)=L\displaystyle f(t)=L.
That is the statement of the intermediate value theorem.

Yes .. but the OP said..
I don't understand the formal definition of the intermediate value theorem

and therefore - I wanted to know exactly which word is "confusing" to him!
 
pka gave the formal definition. What part do you not understand? . It basically says that if you drive your car from 50 mph to 75 mph then you did every speed in between. You did, even if for just an instant, travel at 67.45 mph!
 
Top