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

they gave you everything you need to do that ... f(0) = 2 and f'(0) = -3

b. Is there sufficient information to determine whether or not the graph of

has a point of inflection when

? Explain your answer.

what do you need to tell you that f(x) has inflection point(s) ?
c. Given that

, write an equation of the line tangent to the graph of

at the point where

another tangent line problem ... they gave you the point, g(0) = 4 , all you need is the value of g'(0) for the slope of the line ... can you find that?

d. Show that

. Does

have the local maximum at

? Justify your answer.

fairly straightforward ... they gave you g'(x) and want you to find g''(x) simplified to the given form.