AP Exam Practice Packet : Free Response

i cant seem to understand this concept, its very confusing, can anyone give me any tips?

4. Suppose that the function has a continuous second derivative for all , and that , , and . Let be a function whose derivative is given by for all .

a. Write an equation of the line tangent to the graph of the at the point where

b. Is there sufficient information to determine whether or not the graph of has a point of inflection when ? Explain your answer.

c. Given that , write an equation of the line tangent to the graph of at the point where

d. Show that . Does have the local maximum at ? Justify your answer.

Some help would very much be appreciated.