# Thread: Where to even begin with this piecewise monstrosity?

1. ## Where to even begin with this piecewise monstrosity?

You don't really have to do these problems for me, but at least explain how to even comprehend this. Thanks!

2. ## Re: Where to even begin with this piecewise monstrosity?

This is all pretty straightforward

$B(r) = \begin{cases}\dfrac{B_0}{r_0}r &r \leq r_0 \\r_0 B_0 \dfrac{1}{r} &r_0 < r \end{cases}$

So we see that $B(r)$ is linear in $r$ for $r\leq r_0$ and is proportional to $\dfrac 1 r$ for $r > r_0$

We also note that $B(r_0) = B_0$

Given above it really should be pretty clear which graph corresponds to $B(r)$ (hint: C)

Is $B(r)$ continuous at $r_0$? Well look at it. Is it? (hint: B)

Does the derivative exist at $r_0$ It should be pretty clear that D is correct. Functions with kinks in them aren't differentiable at the kink.

3. ## Re: Where to even begin with this piecewise monstrosity?

Much appreciated.