Suppose f is differentiable. Prove that
exists, where g is a nonzero function of h such that and find the value of .
I think I need to change the terms of the limit from h to g(h) going to zero, not sure how to though.
Any thoughts?
Suppose f is differentiable. Prove that
exists, where g is a nonzero function of h such that and find the value of .
I think I need to change the terms of the limit from h to g(h) going to zero, not sure how to though.
Any thoughts?
May be that a little problem exist in this case. If is differentiable in , then...
(1)
... i.e. both the derivatives 'from left' and 'from wright' exist and they are equal. In the proposed 'alternative' if , for instance, is , then is...
(2)
... so that we have no information about the derivative 'from left' of in ...
Kind regards