Which of the following are true and which false? Give proofs or counterexamples.
I said this was false and my counterexample was .Quote:
i). If (this is a mapping, I couldn't quite find the right arrow) is continous at c then f is differentiable at c.
This function is continous at 0 but which is not differentiable at 0.
I'm not really sure about this one.Quote:
ii). If and such that then f is differentiable at c if:
a). Z is bounded
b). g is differentiable at c with g'(c)=0 and
I think it's true but I don't know how to prove it. (Wondering)
I put false and used the counterexample when c=0.Quote:
iii). In ii) f is differentiable assuming only (a) and (c).
Once again I put false and used the counterexample where c=0.Quote:
In ii). f is differentiable assuming only (a) and (b).
This is false because could be discontinous.Quote:
In (ii). f is differentiable assuming only (b) and (c).
My counterexample was at c=0.
Here and .
are these correct?