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swin2013
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For the function graphed, are the following nonzero quantities positive or negative?
 one year ago
 one year ago
swin2013 Group Title
For the function graphed, are the following nonzero quantities positive or negative?
 one year ago
 one year ago

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swin2013 Group TitleBest ResponseYou've already chosen the best response.0
dw:1354148967410:dw a) f(2)  positive b) f'(2)  ? c) f''(2)  ?
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
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.
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
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?
 one year ago

swin2013 Group TitleBest ResponseYou've already chosen the best response.0
dw:1354149764955:dw
 one year ago

swin2013 Group TitleBest ResponseYou've already chosen the best response.0
lol it's suppose to look like a the tip of a parabola
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
So a horizontal line represents what kind of slope? :D
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
f'(2) is zero :) we can tell that since we drew a tangent line. It is neither positive nor negative, right? :D
 one year ago

swin2013 Group TitleBest ResponseYou've already chosen the best response.0
so neither are postive or negative?
 one year ago

swin2013 Group TitleBest ResponseYou've already chosen the best response.0
except for f(2)? Which is negative.. lol i never meant to put postive
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
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. \[f''>0 \qquad \rightarrow \qquad \text{Concave Up}\]\[f''<0 \qquad \rightarrow \qquad \text{Concave Down}\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
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''?
 one year ago

swin2013 Group TitleBest ResponseYou've already chosen the best response.0
it's increasing?
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
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.
 one year ago

swin2013 Group TitleBest ResponseYou've already chosen the best response.0
so f(2) is negative, f'(2) is positive, therefore f''(2) is also positive :D
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Why was f'(2) positive? :o
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
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).
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
f(2) Negative f'(2) Zero f''(2) Positive
 one year ago

swin2013 Group TitleBest ResponseYou've already chosen the best response.0
ohhh... it's because they asked if they're positive or negative lolll
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Yah, these kinds of uhhh graphs dealing with derivatives can be quite tricky c:
 one year ago

swin2013 Group TitleBest ResponseYou've already chosen the best response.0
Lolll ahhh well thank you again!! you're a life saverrrr!
 one year ago
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