How do I measure function's increasing intervals length?

[Goethe10]

Is there a formula or something? When I solve quadratic equation I get two roots of x1 and x2. how can I find out the length? Thank you

 

[Ackbach]

It's not quite clear what you're asking. Are you asking the distance between x_{1} and x_{2}?

 

[Goethe10]

Yes I am, sorry for confusion

 

[Ackbach]

Well, on the face of it, just form the difference |x_{1}-x_{2}|. Or are you trying to determine the distance between the roots without knowing the roots? Perhaps just from the original quadratic?

 

[Goethe10]

I'll try to explain something, excuse my English.
So the original equation is
-1/3x^3+1/2x^2+2x-5
With derivation I get
-x^2+x+2
The roots are 1 and -1
and I need to find length of increasing function

 

[SteamKing]

Still not clear. By taking the first derivative of the function and finding out where the derivative is zero, then this indicates where the original function has a local maximum or minimum point.

If it's not easy for you to ask your question in English, try asking it in your native language. There may be someone else on PF who can help.

 

[Goethe10]

I don't think so, ANYWAY I figured it out
I'll try to clear things up about what I was trying to say.. so when I find x1 and x2
Say x1 = -2 and x2 = 5
the formula for this was = I need to take biggest root and subtract the other root.
So 5 - ( - 2) = 7.

 

[HallsofIvy]

That's exactly what you were told before : |x_1- x_0|.