hey guys and gals! i'd greatly appreciate if you helped me with some insight on these problems.

1) f is continuous on [0,3] because there are no breaks, holes, asymptotes or gaps. f is differentiable on (0,3) because there are no discontinuities previously mentioned or sharp turns.

So there exists a

So now I found the derivative to find what c value equals f ' (c).

So I set f ' (c) and f ' (x) equal to each other:

Then I put the

on the bottom:

I cross multiplied:

Then I thought take ln of both sides, but ln(-6) gives an error. Why doesn't this work?