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 $\displaystyle f$ has a continuous second derivative for all $\displaystyle x$, and that $\displaystyle f(0)=2$, $\displaystyle f'(o)=-3$, and $\displaystyle f''(0)=0$. Let $\displaystyle g$ be a function whose derivative is given by $\displaystyle g'(x)=e^{-2x} (3f(x)+2f'(x))$ for all $\displaystyle x$.

a. Write an equation of the line tangent to the graph of the $\displaystyle f$ at the point where $\displaystyle x=0$

b. Is there sufficient information to determine whether or not the graph of $\displaystyle f$ has a point of inflection when $\displaystyle x=0$? Explain your answer.

c. Given that $\displaystyle g(0)=4$, write an equation of the line tangent to the graph of $\displaystyle g$ at the point where $\displaystyle x=0$

d. Show that $\displaystyle g''(x)=e^{-2x} (-6f(x)-f'(x)+2f''(x))$. Does $\displaystyle g$ have the local maximum at $\displaystyle x=0$? Justify your answer.

Some help would very much be appreciated.