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

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

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1f'(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.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw: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?

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0lol it's suppose to look like a the tip of a parabola

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1So a horizontal line represents what kind of slope? :D

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

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0so neither are postive or negative?

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

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1f'' 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. \[f''>0 \qquad \rightarrow \qquad \text{Concave Up}\]\[f''<0 \qquad \rightarrow \qquad \text{Concave Down}\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1We 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''?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Well... 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.

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

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Why was f'(2) positive? :o

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1We 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).

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1f(2) Negative f'(2) Zero f''(2) Positive

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0ohhh... it's because they asked if they're positive or negative lolll

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

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0Lolll ahhh well thank you again!! you're a life saverrrr!
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