Question

PLEASE HELP @solomonzelman

Answer 1

@mathmale @Compassionate @SolomonZelman

Answer 2

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.

Answer 3

@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)

Answer 4

What I don't understand is how to figure out the concavity if you don't know the graph of f ''

Answer 5

you know the graph of f'.

Answer 6

@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

Answer 7

Ah, I see. And where on f ' will f '' be zero?

Answer 8

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)

Answer 9

((because f" is derivative/slope in relation to f', just as f' is derivative/slope in relation to f))

Answer 10

I hope I am not being too long and confusing, although I probably am.

Answer 11

will f '' be zero where f ' is zero?

Answer 12

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?)))

Answer 13

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

Answer 14

`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

Answer 15

Thank you so much for both of your guys' help. I understand now!

Answer 16

Can you help with another one? (i'll tag you)

Answer 17

sure, go ahead