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Home  Continuous Functions Continuity Examples Example 3 |
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Example 3
The next two examples give functions which are continuous but not differentiable at a point c. The function y = x1/3 is continuous but not differentiable at x = 0. (See Figure 3.4.4(a).) We have seen before that it is not differentiable at x = 0. It is continuous because if Δx is infinitesimal then so is Δy = (0 + Δx)1/3 - 01/3 = (Δx)1/3.
Figure 3.4.4
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Last Update: 2010-11-25