15. Which of the following functions is continuous everywhere, but has at least one point where it is not differentiable?
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A. tan x |
B. |x|/x |
C. sin x |
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D. e-x |
E. x1/3 |
Solution: The answer is E
The function tan(x) has a discontinuities at Pi/2, 3Pi/2 .. ; The function |x|/x is not continuous at x = 0. The only three functions above that are continuous everywhere are sin x, e-x, and x1/3. Their corresponding derivatives are,
However, the only derivative that is not defined at x = 0 is that of x1/3. Hence, x1/3 is the only function that is continuous everywhere, but has at least one point where its is not differentiable.