Questions: For the graph shown below, find all values of x for which f(x) is not differentiable.

Transcript text: For the graph shown below, find all values of $x$ for which $f(x)$ is not differentiable.

Solution

Solution Steps

Step 1: Identify Points of Discontinuity

Examine the graph to identify any points where the function is not continuous. A function must be continuous to be differentiable. In this graph, there are no points of discontinuity.

Step 2: Identify Sharp Corners or Cusps

Look for points where the graph has sharp corners or cusps, as these are points where the function is not differentiable. In this graph, there are sharp corners at $ x = 1 $ and $ x = 3 $.

Step 3: Identify Vertical Tangents

Check for any points where the tangent to the graph is vertical, as the function is not differentiable at these points. In this graph, there are no vertical tangents.