## baldymcgee6 3 years ago What two graphical features may occur at a critical value that does not generate a maximum or a minimum?

horizontal and vertical asymptotes

2. baldymcgee6

nope

3. baldymcgee6

@zepdrix

4. jim_thompson5910

5. baldymcgee6

the answer is a sharp corner or an inflection point. Such a general question, I think it's just for single variable

6. jim_thompson5910

true, that's another name for it saddle points apply to 1 variable functions as well

7. baldymcgee6

What is a "sharp corner" is that like a cusp?

8. jim_thompson5910

yes

9. jim_thompson5910

something like this |dw:1353381760893:dw|

10. baldymcgee6

same same? Could it not be a vertical asymptote as well? Or what about a single point hole?

11. jim_thompson5910

well here's another example of a sharp point |dw:1353381837898:dw|

12. jim_thompson5910

aka, the absolute value function

13. baldymcgee6

hmmm... interesting.

14. jim_thompson5910

a sharp point is basically a point that is non-differentiable, but the function is still continuous

15. jim_thompson5910

well that's part of the definition anyway

16. baldymcgee6

So why does it show up as a critical value?

17. jim_thompson5910

well if there's a horizontal tangent at this sharp point or saddle point, then the derivative function will have a zero at that point

18. jim_thompson5910

so if you look at the derivative alone, you'll see more critical points than extrema

19. baldymcgee6

If a cusp is non-differentiable are we able to still put a tangent line there?

20. jim_thompson5910

not sure what you mean

21. baldymcgee6

You said at the sharp point it is continuous but not differentiable. I thought we had to be able to differentiate it to have a slope of 0 there?

22. jim_thompson5910

true, now I'm not sure, maybe there are some other criteria for a point to be considered a critical point

23. baldymcgee6

|dw:1353382502904:dw||dw:1353382579141:dw|This produces a local minimum at (0,0), so in this case, the cusp produced a minimum.

24. jim_thompson5910

so maybe a cusp/sharp point isn't a point in which is a critical point, but not an extrema

25. baldymcgee6

Who knows, I'm going to try and find some solid definitions.

26. jim_thompson5910

alright

27. baldymcgee6

thanks for the input.

28. jim_thompson5910

np