Graph of f related to behavior of f' and f''

[Sophie]

Happy Easter everyone

The following relate to drawing graphs of f using f' and f''

1) What are the possibilities of f when f' is undefined at a point x?

2) What are the possibilities of f when f'' is undefined at a point x?

3) What are the possibilities of f when f' and f'' are undefined at a point x?

Questions are coming up in my text and the ones I am getting wrong are related to the above. When I go through the worked examples of my text it makes sence however I repeat the same mistake. My text does not define the above 3 points and if someone could claify them, I am hoping I will stop making silly mistakes.

Thanks Sophie

 

[stapel]

1) You've done graphs, such as y = |x| or y = 1/x, where the first derivative wasn't defined at one point or another. What had this meant? (Hint: What aspect of the original function does the first derivative represent?)

2) What sorts of graphs have you drawn, for which the second derivative was not defined at one or another point?

3) Out of the possibilities you've considered for (1) and (2), are there any that apply to only one of (1) and (2)? Consider the others when answering (3).

Eliz.

 

[Sophie]

Thanks

I am on the right track, I guess I just have to try more examples and see if it all comes together.

Sophie