Question:
For what value of \(x\), \(f(x) = |2x - 7|\) is not differentiable.
Answer:
We need to find the input value for which the function will not be differentialable. In other words, the point where the function has a break or sharp edge (cusp; there are infinte many tangents available at that point)
\[ f(x) =\left\{
\begin{array}{ll}
2x-7 & x \leq \dfrac{7}{2}\\
7-2x & x < \dfrac{7}{2}\\
\end{array}
\right.\]
Hence, for the value \(x=\frac{7}{2}\), the function is not differentialable.
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