Determine whether the following statements are true and give an explanation or counterexample.

a. The function f|x2 = |2x + 1| is continuous for all x; therefore, it is differentiable for all x.

b. If d/dx (f(x)) = d/dx (g(x)), then f = g.

c. For any function f, d/dx |(f(x)| = |f'(x)|.

d. The value of f'(a) fails to exist only if the curve y = f(x) has a vertical tangent line at x = a.

e. An object can have negative acceleration and increasing speed.