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Graphical Solution of Equations

The function ...

Question

The function f(x) is given as
$f (x) = min | x |, | x - 2 |, 2 - | x - 1 |$ the number of points where $f (x)$ is not differentiable are

One

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Five

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Seven

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Three

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Solution

The correct option is B Five
$f (x) = min | x |, | x - 2 |, 2 - | x - 1 |$

So the resulting graph is

So there are five points of non-differentiability
$x = {- \frac{1}{2}, 0, 1, 2, \frac{5}{2}}$

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