Graphing the function f based on the graph of f prime.

Thread starter BlackMamba
Start date Nov 26, 2005
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Function Graph Graphing Prime

In summary, the purpose of graphing the function f based on the graph of f prime is to visualize and understand the relationship between a function and its derivative. To graph the function f, plot the points of f prime and use the slope of the tangent line at each point to determine the direction and concavity of f. The critical points of f can be found by looking at the x-values of the points where f prime is equal to 0 or undefined. It is possible for a function to have multiple graphs based on the same graph of f prime, and this can be helpful in real-world applications such as analyzing motion in physics or making decisions in economics.

Nov 26, 2005

BlackMamba

Hello,

I have this problem that I completed. I was hoping somebody could just let me know, based on my answers if the graph I have drawn looks to be correct? I would really appreciate it.

Thanks to anyone who replies.

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Nov 26, 2005

HallsofIvy

Science Advisor

Homework Helper

Looks good to me!

Nov 26, 2005

BlackMamba

Thanks HallsofIvy, it's appreciated for sure.

1. What is the purpose of graphing the function f based on the graph of f prime?

The purpose of graphing the function f based on the graph of f prime is to visualize and understand the relationship between a function and its derivative. This can help in analyzing the behavior and properties of the original function.

2. How do I graph the function f based on the graph of f prime?

To graph the function f based on the graph of f prime, first plot the points of f prime on a coordinate plane. Then, use the slope of the tangent line at each point to determine the direction and concavity of f. Finally, connect the points to create a smooth curve that represents the graph of f.

3. Can I use the graph of f prime to find the critical points of f?

Yes, the critical points of a function f can be found by looking at the x-values of the points where f prime is equal to 0 or undefined. These points represent the local extrema and points of inflection of f.

4. Is it possible for a function to have multiple graphs based on the same graph of f prime?

Yes, it is possible for a function to have multiple graphs based on the same graph of f prime. This can occur when the original function has different intervals of increasing and decreasing behavior, leading to different shapes of the graph for each interval.

5. How can graphing the function f based on the graph of f prime be helpful in real-world applications?

In real-world applications, the graph of a function and its derivative can provide valuable information about the behavior and trends of a system. For example, in physics, the derivative of a position function represents velocity, and the graph of the derivative can help analyze the motion of an object. Additionally, in economics, the derivative of a cost function represents marginal cost, and the graph of the derivative can assist in decision-making for businesses.