I would like to know, when could Rolle's theorem be applied? The book focused on it briefly(not enough), Well, here is a problem: f(x)=(x^(1/3))-1 on[-8,8]. (oddly enough), it only ask if Rolle's theorem can be applied in this case?
I would like to know, when could Rolle's theorem be applied? The book focused on it briefly(not enough), Well, here is a problem: f(x)=(x^(1/3))-1 on[-8,8]. (oddly enough), it only ask if Rolle's theorem can be applied in this case?
Rolle's Theorem
Let $\displaystyle f:[a,b]\to\mathbf{R}$ a function such that:
1) $\displaystyle f$ is continuos on $\displaystyle [a,b]$;
2) $\displaystyle f$ is differentiable on $\displaystyle (a,b)$;
3) $\displaystyle f(a)=f(b)$.
Then, exists at least one point $\displaystyle c\in(a,b)$ such that $\displaystyle f'(c)=0$.
Now, your function is $\displaystyle f:[-8,8]\to\mathbf{R},f(x)=\sqrt[3]{x}-1$.
Which hypothesis is not verified?
Au contrare!
-Dan