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Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then

  1. $f$ is uniformly continuous.
  2. $f$ is continuous, but not differentiable at $x=0$.
  3. $f$ is differentiable and $f ' $ is continuous.
  4. $f$ is differentiable, but $f ' $ is discontinuous at $x=0$.
asked in Calculus by Veteran (28.1k points)   | 152 views

2 Answers

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f is differential & first derivative of f is discontinuous at x =0
answered by Veteran (43.7k points)  
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The graph for $f(x) = |x|^{\frac{3}{2}}$ looks like :

And the plot of its derivative is :

Clearly : option D

f(x) is not continuous because the domain is all R, but the plot is only possible for positive real numbers.

answered by Loyal (4k points)  
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