1. Intermediate Value Theorem

Hi!

Considering the function

f(x) =

-x + x + 4 if x > -1
4 if x = -1
3 - x if x < -1

I was asked to show that the equation f(x) = -1 has a solution between 1 and 2. (Function was already determined to be continuous.)

For my solution:

f(x) = -(1)^3 + 1 + 4 = 4
f(x) = -(2)^3 + 2 + 4 = -2

Given that f(x) is a continuous function and f(2) < -1 < f(1) then by the intermediate value theorem there exists some number c such that f(x) = -1

Unfortuntely, I only recieved half credit for the answer. Is there something I missed? Was "f(2) < -1 < f(1)" the issue? Should I have manipulated my equations so that 0 would have been the center number?
(ex. f(x) -x^3 + x + 4 + 1 = 0 )

Any suggestions would be fantastic!
Thank you!

2. Originally Posted by strgrl
Considering the function

f(x) =
-x + x + 4 if x > -1
4 if x = -1
3 - x if x < -1
Please look over that definition. There must be a typo in it.

3. Sorry!

f(x) =
-x^3 + x + 4 if x > -1
4 if x = -1
3 - x if x < -1

Thank you.

4. Originally Posted by strgrl
I was asked to show that the equation f(x) = -1 has a solution between 1 and 2. (Function was already determined to be continuous.)
Unfortuntely, I only recieved half credit for the answer. Is there something I missed? Was "f(2) < -1 < f(1)" the issue?
Of course if I were you, I would indeed ask the instructor why.
I can suggest two possible reasons (though I find neither reasonable here).
1) Maybe you were expected to show f was continuous or at least note it.
2) Maybe you were expected to find the actual value such f(c)=-1.