Consider the family of functions F(x) that satisfies F′(x)=2x+1.
(a) Describe the relationship between any two such antiderivatives. Your answer should make explicit reference to how the graphs of the functions are positioned relative to one another.
(b) A particle moving along a line has position described by F(x), and it is known that F(2)=7. Explain how this single condition determines a unique member of the family and write the explicit formula for that particular function.
(c) Suppose instead that the only information given were F′(x)=2x+1 and the fact that the particle passes through the point (2,y0), where y0 is unknown. What additional quantitative information must be supplied to single out a particular solution? Justify your answer.