Derivative of Absolute Function | Calculus

Question:

Evaluate the derivative of \(|x - 3|\) at \(x = -1\)

Answer:

Writing the function in piecewise form, we get \[ f(x) =\left\{ \begin{array}{ll} x-3 & x > 3\\ 3-x & x \leq 3 \\ \end{array} \right.\] For \(x=-1\), we only choose the function when \(x \leq 3\), $$f(-1)=3-(-1)=4$$ $$f'(x)=\frac{d}{dx}(3-x)=-1$$ $$f'(-1)=-1$$