Graph the learning curve L(x) = (x - 2)^3 +8

  • Thread starter Rolando Valdez
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In summary, the conversation is about a learning curve function and graphing it. The function is typically in the form L(x) = (x-a)^n + b, with "a", "b", and "n" being positive constants. The task at hand is to graph the function L(x) = (x - 2)^3 + 8 and potentially find maxima, minima, and points of inflection using derivatives. The person thanks for the advice and agrees to complete the task.
  • #1
having trouble getting started on this problem. I don't really know what to do first.

A learning curve is a function L(x) that gives the amount of time that a person requires to learn "X" pieces of information. Many learning curves take the form L(x) = (x-a)^n + b (for x>0 or x=0), where "a", "b" and "n" are positive constants. Graph the learning curve L(x) = (x - 2)^3 +8.
 
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  • #2
Just draw the curve. That's all you're being asked to do.
 
  • #3
It's just a cubic polynomial. Depending on what they expect, you may have to use the various derivatives to find maxima, minima, and/or points of inflection. Find them, and draw it!
 
  • #4
Thanks for the advice. Will do.
 

1. What is the purpose of graphing the learning curve L(x) = (x - 2)^3 +8?

The purpose of graphing the learning curve is to visually represent the relationship between the input, x, and the output, L(x), in order to better understand how the function behaves and changes over the input values.

2. How do I plot the points for the learning curve L(x) = (x - 2)^3 +8?

To plot the points, choose a range of input values for x, plug them into the function, and calculate the corresponding output values for L(x). Then, plot these points on a coordinate plane and connect them with a smooth curve.

3. What does the "x - 2" term in the learning curve L(x) = (x - 2)^3 +8 represent?

The "x - 2" term represents a shift of the curve to the right by 2 units on the x-axis. This means that the graph will have a point of inflection at x = 2 and the curve will be steeper on the right side compared to the left side.

4. Can the learning curve L(x) = (x - 2)^3 +8 have negative values?

Yes, the learning curve can have negative values. This will occur when the input value, x, is less than 2. In this case, the output value, L(x), will be negative due to the addition of 8.

5. How can I use the learning curve L(x) = (x - 2)^3 +8 to make predictions?

To make predictions, you can use the graph to estimate the output value, L(x), for a given input value, x. You can also use the slope of the curve to determine the rate of change of the function, which can help in predicting future values.

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