Quote:

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

c). g(c)=0;

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).

and .

Once again I put false and used the counterexample where c=0.Quote:

In ii). f is differentiable assuming only (a) and (b).

Where and

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?