Posted by **Meera** on Sunday, December 9, 2012 at 8:59pm.

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.

- calc -
**Damon**, Sunday, December 9, 2012 at 10:01pm
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

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