9. Which of the following functions are differentiable on the interval (-1,1)
?
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A. I and II only |
B. I and III only |
C. II and III only |
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D. I, II, and III |
E. The correct answer is not given by A, B, C, or D. |
Solution: The answer is B
The absolute value function abs(x) = |x| is differentiable for all x except x = 0, so f(x) is differentiable for all x except x = 5/3. In particular, it is differentiable on (-1, 1).
The function g(x) defined above has a jump discontinuity at 0, so is not differentiable at x = 0.
The function h(x) has the property that h'(x-)=-2x- = 0 = 2x+ = h'(x+), so is differentiable at 0. It is also differentiable at all other x in (-1, 1).