Suppose that f has a continuous second derivative for all x, and that f(0) = 1, f '(0) = 2,
and f ''(0) = 0.
Does f have an inflection point at x = 0? Explain your answer.
Let g'(x) = (3(x^2) + 2)f(x) + (x^3 + 2x + 5)f '(x). The point (0, 5) is on the graph of g. Write the
equation of the tangent line to g at this point.
Use your tangent line to approximate g(0, 3).
I'm just not sure where to even begin with this problem. I have never had a problem like this and it seems so overwhelmingly complicated. If anyone wants to help me out, it would be much appreciated.
I think the answer to the first part is yes, because the second derivative indicates inflection points or changes in concavity. So if it is at zero, then it has to be changing from concave up to concave down or concave down to up...