StudyGurl14
  • StudyGurl14
PLEASE HELP @solomonzelman
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
StudyGurl14
  • StudyGurl14
1 Attachment
StudyGurl14
  • StudyGurl14
@mathmale @Compassionate @SolomonZelman
SolomonZelman
  • SolomonZelman
Inflection point is a point where the function changes concavity. The slope of f is decreasing, and now it is increasing (or vice versa). You are already given the graph of the slope/(derivative) of the function. So, like I have seen in previous replies to your question (posted before), it does seem to be that the point with horizontal tangents (x=2, 4) seem to be the inflection points.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

jim_thompson5910
  • jim_thompson5910
@SolomonZelman is correct f '' is the derivative of f ' to find the inflection points of f, you need to look at where f '' is zero. This happens exactly at the same points where the slope of the tangent line on f ' is zero (ie where there's a horizontal tangent)
StudyGurl14
  • StudyGurl14
What I don't understand is how to figure out the concavity if you don't know the graph of f ''
SolomonZelman
  • SolomonZelman
you know the graph of f'.
jim_thompson5910
  • jim_thompson5910
@StudyGurl14 if f ' is decreasing then f '' will be negative ----> concave down region on f if f ' is increasing then f '' will be positive ----> concave up region on f
StudyGurl14
  • StudyGurl14
Ah, I see. And where on f ' will f '' be zero?
SolomonZelman
  • SolomonZelman
What is concavity? That is the point when the slope starts increasing and starts decreasing or Vice Versa. Note, I used not "function decreasing/increasing" but "slope increasing decreasing" and that is different. Function {in/de}crease means slope is pos/neg. Slope {in/de}crease means the slope is {becoming larger/ becoming negative} So you can view you graph of f' as if it is f, and view the question as just "when will change increase/decrease" (i.e. when will the function stop having neg slope and change to positive slope or Vice Versa)
SolomonZelman
  • SolomonZelman
((because f" is derivative/slope in relation to f', just as f' is derivative/slope in relation to f))
SolomonZelman
  • SolomonZelman
I hope I am not being too long and confusing, although I probably am.
StudyGurl14
  • StudyGurl14
will f '' be zero where f ' is zero?
SolomonZelman
  • SolomonZelman
If you see that f' is increasing till some x=a, and starts to decrease. (or vice versa) then x=a is an inflection point. 9((do you need to find the y-coordinate too?)))
jim_thompson5910
  • jim_thompson5910
f '' describes the slope of the tangent lines on f ' wherever there's a horizontal tangent on f ', the value of f '' will be 0 (horizontal lines ---> slope is 0) see the attached image
jim_thompson5910
  • jim_thompson5910
`will f '' be zero where f ' is zero?` no, we see that f ' is zero at x = 5 but the slope of the tangent line is NOT zero. So f '' will be some positive number and not zero
StudyGurl14
  • StudyGurl14
Thank you so much for both of your guys' help. I understand now!
StudyGurl14
  • StudyGurl14
Can you help with another one? (i'll tag you)
jim_thompson5910
  • jim_thompson5910
sure, go ahead

Looking for something else?

Not the answer you are looking for? Search for more explanations.