How do I answer this?

9514 1404 393

  A.  (-∞, ∞)

  B.  (-∞, 0) U (0, ∞)

Step-by-step explanation:

A. Though the attached calculator disagrees, the value of the derivative of f(x) is actually defined at x=0. Its value is 0. There is a discontinuity in the second derivative at x=0, but both the derivative and the function are continuous there.

  differentiable on (-∞, ∞)

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B. The derivative is discontinuous at x=0, so is undefined there. The function is differentiable everywhere else.

   differentiable on (-∞, 0) U (0, ∞)

_____

The graphs of f(x) and its derivative are red and dotted orange, respectively.

The graphs of g(x) and its derivative are purple and dotted blue, respectively.

There are overlaps, which is why we chose to make some graphs dotted.

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.

3

step-by-step explanation: