Need Help with First/Second/Third Derivative relation

In summary, the conversation is about determining the value of the first derivative at x=1.2 for a given function. The options provided are 0<f '(1.2)<1.6, 1.6<f '(1.2) <1.8, 1.8< f '(1.2) <2.0, and f '(1.2)>2.0. The person is unsure of the correct answer and suggests graphing the points or using rise over run to determine the slopes of the line segments connecting the given points.
  • #1
tangents
21
0
Hello all,

Well I am kind of stumped on this question and was hopeing for somr guidance.

X 1.1 1.2 1.3 1.4
f(x) 4.18 4.38 4.56 4.73

F is obviously a function and f ''(x)<o for all x in the closed interval. The question asks which of the following has to be for f '(1.2)?

1) f '(1.2)<0 This can't be it becuase f(x) is positive
2) 0<f '(1.2)<1.6
3) 1.6<f '(1.2) <1.8
4) 1.8< f '(1.2) <2.0
5) f '(1.2)> 2.0 This one is saying that the slope at 1.2 is greater than 2, but i suppose the only way to be certain is to graph the points and find out.As for the rest I'm not entirely sure but hope you guys can assist me ; ;
 
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  • #2
tangents said:
1) f '(1.2)<0 This can't be it becuase f(x) is positive

The reason you stated does not guarantee that the first derivative is positive. A positive valued function can have a negative slope and thus a negative first derivative.

5) f '(1.2)> 2.0 This one is saying that the slope at 1.2 is greater than 2, but i suppose the only way to be certain is to graph the points and find out.

You could graph them, or you could use rise over run.

I believe the problem intends for you to calculate the slopes of each of the lne segments connecting the points given in the problem and using those values to determine limiting values for the derivative at the indicated point.
 

1. What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is essentially the slope of a tangent line to the function at that point.

2. What is the first derivative?

The first derivative is the derivative of a function with respect to its input variable. It represents the rate of change of the function at any given point and can be used to find the slope of the tangent line at that point.

3. How is the second derivative related to the first derivative?

The second derivative is the derivative of the first derivative. It represents the rate of change of the slope of the tangent line at a specific point. In other words, it shows how the slope of the tangent line is changing at that point.

4. What is the third derivative?

The third derivative is the derivative of the second derivative. It represents the rate of change of the curvature of a function at a specific point. It can be used to determine the concavity of the function at that point.

5. How are first, second, and third derivatives related?

The first, second, and third derivatives are all related to each other as they represent different aspects of a function's rate of change. The first derivative represents the slope, the second derivative represents the rate of change of the slope, and the third derivative represents the rate of change of the curvature. Together, they provide a comprehensive understanding of how a function is changing at a specific point.

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