Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then
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.
More insight here,
http://www.wolframalpha.com/input/?i=y%3D|x|^(3%2F2)
I think answer should be B
Why left part is not imaginary like this
What will be the definition of this function
$$f(x) = \begin{cases} x^{3/2} &\text{ for }x \geq 0 \\ (-x)^{3/2} &\text{ for } x<0 \end{cases}$$
OR
$$f(x) = \begin{cases} x^{3/2} &\text{ for }x \geq 0 \\ -(x^{3/2}) &\text{ for } x<0 \end{cases}$$ ?
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