Let
g(x)=∣x2−4∣+2x,x∈R.
Throughout, show algebraic work leading to all conclusions.
(a) Express g as a piecewise–defined function without absolute value bars.
(b) For each piece, compute g′(x).
(c) Solve g′(x)=0 on each open interval where g is differentiable. List all real solutions.
(d) Identify every point at which g′(x) is not defined but g is defined. Explain why the derivative fails to exist at each such point.
(e) Combine your results from parts (c) and (d) to state all critical points of g on R. No classification of extrema is required.