9514 1404 393
Answer:
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, ∞)
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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.
