Draw graph given f'(x), f''(x), domain, etc. Please check?

In summary, the conversation discusses the process of sketching a graph based on given information. The first speaker mentions sketching a graph with slightly curved lines, and then asks for feedback on its accuracy. The second speaker points out areas of concern, such as interpreting concavity and drawing points and curves for the second derivative. They also mention the use of labels and the dot convention. Overall, they ask for confirmation on the accuracy of their sketch.
  • #1
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1. I was asked to roughly sketch a graph given the information seen, in the below picture, to the right of the graph.

28rcitw.jpg


2. My actual graph is done by hand and the lines are not as straight, but the general shape is the same.

Does it look approximately right?

The areas I am worried about are:
a) when it specifies being concave of convex between certain intervals: whether it means completely visible between those intervals as concave/convex or just beginning to appear concave/convex

b) where it says "no limit of y x -> -2" exists, whether or not I should have drawn it the same angle as I did, or started the one to the left of -2 from a different angle.
 
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  • #2
First, label the axis, and adopt the dot convention where a solid dot contains that point and a circle indicates a hole. Everything looks okay until you get to the second derivitive/concavity. The points where the second derivative would be zero (in between the domain of concavity given) should be points, and after that it should have a curve. For instance, when it says that from 5 to 10 (for example) f'' is positive, that means the graph should "open upwards" from 5 to 10, and if f'' is negative from 10 to infinity, then it should curve back downwards.
 
  • #3
Thanks, QuarkCharmer.

To you or anyone who sees, I'm just wondering if this one is more accurate? Again, aside from the straight line, which I know means f"(x) = 0.

2cd9hz.jpg
 

FAQ: Draw graph given f'(x), f''(x), domain, etc. Please check?

What is the purpose of drawing a graph given f'(x), f''(x), domain, etc.?

The purpose of drawing a graph given f'(x), f''(x), domain, etc. is to visually represent the behavior and characteristics of a function. This can help in understanding the function's rate of change, concavity, and other important features.

How do I find the domain of a function?

To find the domain of a function, you must first determine the values of x that are allowed in the function. This means looking for any restrictions or limitations on the x-values, such as division by zero or taking the square root of a negative number. The domain will be all the x-values that satisfy these restrictions.

What does f'(x) represent in a graph?

f'(x) represents the derivative of the function f(x), or the rate of change of the function at a specific point. In a graph, f'(x) can be represented by the slope of the tangent line at that point.

How do I find the critical points of a function?

The critical points of a function are the points where the derivative, f'(x), is equal to zero or does not exist. To find these points, set the derivative equal to zero and solve for x. These critical points can then be used to determine the function's concavity and identify any local extrema.

What is the relationship between f'(x) and f''(x) in a graph?

f'(x) and f''(x) represent the first and second derivatives of a function, respectively. In a graph, f'(x) can be thought of as the slope of the tangent line, while f''(x) can be thought of as the rate of change of the slope. In other words, f''(x) represents the concavity of the function at a specific point.

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