MHB Which Points Have Specific Characteristics for f', f'', and f'''?

  • Thread starter Thread starter karush
  • Start date Start date
  • Tags Tags
    Graph
Click For Summary
The discussion focuses on identifying specific characteristics of points labeled A, B, C, D, and E in relation to the derivatives f', f'', and f'''. Points B and E are identified as having non-zero f' and f'' with the same sign. Points A, C, and D are debated for having at least two of f, f', and f'' equal to zero, with particular scrutiny on point D regarding its slope. Participants express uncertainty about the definitions of zeros and inflection points, leading to differing opinions on whether points C and D should be included in the selection. The conversation emphasizes the importance of re-evaluating the characteristics of these points based on their slopes and curvature.
karush
Gold Member
MHB
Messages
3,240
Reaction score
5
View attachment 442

Which of the points labeled by a letter have

(a) $f'$ and $f''$ non-zero and the same sign B, E

(b) At least two of $f, f', f''$ equal to zero A, C, D

not sure if these selections were correct and was ? about D in the slope appears to be zero

f' is about slope f'' is about inflection pts and increasing and decreasing I presume

thanks ahead.
 
Physics news on Phys.org
I agree with your answer for a), but I would remove one of the points from b). I don't want to say which, as I want you to re-examine on your own.
 
well, i would remove D since has neither zero on x or y-axis but my ? is it does have a m=0

not absolute sure what is meant by zero's here
 
I would keep D, as the slope appears to be zero there, and it appears that curvature is changing there also.
 
ok how about C since at f it has x=0 at f' it has m=0 but f'' there is no inflection pt.
or is it ...
 
Yes, I think C does not belong, since at that point it appears to me that 0 < f and f'' < 0.
 
Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
View full post »

Similar threads

MHB Is f(x)=ln(x)/x Increasing or Decreasing?
  • · Replies 1 ·
Replies
1
Views
2K
MHB 141.30 how many points of inflection will the graph of the function have
  • · Replies 3 ·
Replies
3
Views
1K
MHB 2.2.212 AP Calculus Exam problem find increasing interval
  • · Replies 2 ·
Replies
2
Views
2K
MHB Is the Inflection Point at x = 7 Incorrect?
  • · Replies 5 ·
Replies
5
Views
2K
I Finding the derivative of a characteristic function
  • · Replies 5 ·
Replies
5
Views
3K
Prove that solutions to autonomous first order DE can't have local maxima
  • · Replies 2 ·
Replies
2
Views
1K
The first and second derivatives at various points on a drawn graph
  • · Replies 22 ·
Replies
22
Views
3K
Graphing Derivatives: Concavity and Inflection Points
  • · Replies 4 ·
Replies
4
Views
3K
MHB *find coefficients of cubic f(x) given min max & inflexion pt
  • · Replies 4 ·
Replies
4
Views
26K
The integral of a function ##f(x)## from its graph
  • · Replies 15 ·
Replies
15
Views
2K