Question

Which of these solutions satisfies the Rolle’s Theorem for the function f(x)= x sq.rt. of (x+6) in [-6, 0]?

Answer 1

\[f(x)=x\sqrt{x+6}\] for sure yes?

Answer 2

yes (:

Answer 3

\[f(-6)=f(0)=0\] so you can use rolle's theorem says there is an number c between -6 and for which
\[f'(c)=\frac{3(c+4)}{2\sqrt{c+6}}=0\]

Answer 4

your job is just to solve for c, which you can pretty much do in your head. looks like the solution is
\[c=-4\]

Answer 5

Omg! Thanks so much! It all makes sense now! (: