calc

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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 -

    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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