Using Rolle's Theorem to Prove Cubic has Exactly One Root | Calculus 1 Exercises

[@NitronNeutron]

This really a variation of determining no extrema.

[@NitronNeutron]

I mean f'(x) > 0 so the function is increasing ergo one-to-one and therefore only one real root.

[@punditgi]

Nifty! 🎉😊

[@maximusthegreatest]

I'm still kind of confused on this. If the derivative is greater than 0, why does that say we can't have another root? Is it because once we are moving in a positive direction(positive derivative), to go back to 0 we would need a negative derivative to curve down but since we will never get a negative derivative, we will never cross the x axis again?

[@pratheesh.]

You are correct. Since f'(x) if +ve and f is continuous, f is strictly increasing on the interval.

[@GOJOshen]

pin me please?