Let f(x)=3x2−4x+6. Four candidate functions are proposed:
(a) Differentiate each candidate function, listing the resulting expressions.
(b) Identify every candidate whose derivative equals f(x) for all real x, and justify your conclusion.
(c) Describe, with reference to your results, the role played by an added constant when forming an antiderivative of f. Explain why this constant does not affect which functions qualify in part (b).