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

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In summary, the points labeled B and E have both non-zero $f'$ and $f''$ values with the same sign. The points labeled A, C, and D have at least two of $f, f', f''$ equal to zero, but there may be an error in labeling C as it appears to have 0 < f and f'' < 0. The point D should not be removed as it has a slope of 0 and a changing curvature.
  • #1
karush
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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.
 
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  • #2
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.
 
  • #3
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
 
  • #4
I would keep D, as the slope appears to be zero there, and it appears that curvature is changing there also.
 
  • #5
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 ...
 
  • #6
Yes, I think C does not belong, since at that point it appears to me that 0 < f and f'' < 0.
 

Related to Which Points Have Specific Characteristics for f', f'', and f'''?

1. How do you locate f' on a graph?

To locate f', you need to find the slope of the tangent line at a specific point on the graph. This can be done by taking the derivative of the function at that point. The value of f' will give you the slope of the tangent line at that point.

2. What does f'' represent on a graph?

f'' is the second derivative of the function, which represents the rate of change of the slope of the function. It tells you how the slope is changing at a specific point on the graph.

3. How can you find f''' on a graph?

To find f''', you need to take the derivative of the second derivative of the function. This means taking the derivative of f'' to find the rate of change of the slope of the slope of the function at a specific point on the graph.

4. What does the sign of f' tell us about the graph?

The sign of f' tells us about the direction and steepness of the graph at a specific point. If f' is positive, the graph is increasing at that point. If f' is negative, the graph is decreasing. The magnitude of f' also indicates the steepness of the curve.

5. Why is it important to understand f', f'', and f''' on a graph?

Understanding f', f'', and f''' allows us to analyze the behavior of a function and make predictions about the graph. It helps us determine critical points, inflection points, and concavity of the function. This information is essential in many fields of science and engineering, such as physics, economics, and biology.

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