## swin2013 2 years ago For the function graphed, are the following nonzero quantities positive or negative?

1. swin2013

|dw:1354148967410:dw| a) f(2) - positive b) f'(2) - ? c) f''(2) - ?

2. swin2013

@zepdrix

3. zepdrix

f'(2) represents the SLOPE of the function at that point. So let's draw the line tangent to the curve at f(2) to see what it looks like.

4. zepdrix

|dw:1354149736096:dw| It's kind of hard to tell, based on the sloppy drawing lolol. Was it supppose to be slanted down like that? Or is it suppose to be flat on the bottom at 2?

5. swin2013

|dw:1354149764955:dw|

6. swin2013

lol it's suppose to look like a the tip of a parabola

7. zepdrix

So a horizontal line represents what kind of slope? :D

8. swin2013

f'(2)

9. zepdrix

f'(2) is zero :) we can tell that since we drew a tangent line. It is neither positive nor negative, right? :D

10. swin2013

so neither are postive or negative?

11. swin2013

except for f(2)? Which is negative.. lol i never meant to put postive

12. zepdrix

f'' is a little trickier. There are a couple ways we can determine if it's positive or negative. f'' tells us if the SLOPE is increasing or decreasing. But an easier way to maybe think about it is by referring back to the second derivative test. $f''>0 \qquad \rightarrow \qquad \text{Concave Up}$$f''<0 \qquad \rightarrow \qquad \text{Concave Down}$

13. zepdrix

We can use this information in reverse. In the given problem we KNOW that f(2) lies in an area that is CONCAVE UP. See how it's inside of a bowl shape? So what does that tell us about f''?

14. swin2013

it's increasing?

15. zepdrix

Well... it tells us that f' is increasing c: But based on the little facts I printed a sec ago, it tells us that f'' is GREATER THAN ZERO right? :D or in other words, Positive.

16. swin2013

so f(2) is negative, f'(2) is positive, therefore f''(2) is also positive :D

17. zepdrix

Why was f'(2) positive? :o

18. zepdrix

We determined that the slope is zero. It will increase towards the positive as we move to the right, but it is zero at the point f(2).

19. zepdrix

f(2) Negative f'(2) Zero f''(2) Positive

20. swin2013

ohhh... it's because they asked if they're positive or negative lolll

21. zepdrix

Yah, these kinds of uhhh graphs dealing with derivatives can be quite tricky c:

22. swin2013

Lolll ahhh well thank you again!! you're a life saverrrr!

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