...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.