Question

The graph of \(f\) is given. State, with reasons, the numbers at which \(f\) is not differentiable.

Short answer

The numbers at which \(f\) is not differentiable are \(x = - 4\) and \(x = 0\).

Step-by-step solution

Differentiability of the Function

The function can be defined as a differentiable function if the value of the derivative of that function exists for any particular point within its domain.

Find the numbers at which the function is not differentiable.

The given graph is:

Clearly, at\(x = - 4\), the curve shows the inflection that broke differentiability of this function and at \(x = 0\), the function is discontinuous.

Hence, the numbers at which \(f\) is not differentiable are \(x = - 4\) and \(x = 0\).