Question

Which of the following statements would always be true?
I. If f is differentiable at x = c, then f is continuous at x = c.
II. If f is continuous at x = c, then f is differentiable at x = c.
III. If f is not continuous at x = c, then f is not differentiable at x = c.

Answer 1

Rules
If differentiable, then continuous (hard to define derivative of a function at a point where it jumps)
However if continuous, maybe differentiable maybe not. (example of not is |x| at x = 0
so
1. is true
2. not always
3. is true

logic relation of q 1 to q 3
if a cow, then a mammal hypothesis (assume true)
if a mammal then a cow (false) (converse)
if not a cow, then not a mammal (false)(inverse)
if not a mammal, then not a cow (true)(contrapositive)
see
http://hotmath.com/hotmath_help/topics/converse-inverse-contrapositive.html