Making Piecewise Function Continuous w/ First & Second Derivatives

In summary, the speaker is trying to make a piecewise function continuous at x=0 with first and second derivatives by finding values for a and b. They have successfully made the function continuous by equating the limits of the RHS and LHS and solving for a. However, the limits of the second derivatives for the RHS and LHS are different, causing confusion about the possibility of the problem if the second derivatives are not continuous. The speaker requests more information about the problem, specifically the relationship between a and b and the given formula for the function.
  • #1
Dollydaggerxo
62
0
I have to make a piecewise function continuous with first and second derivatives at x=0 by finding a value for a and b.

I have made the function continuous by equating the RHS and LHS limits and then solving for the variable a.

The limit of the first derivatives of the LHS and RHS are the same, both 0, so that makes the first derivative continuous...

However, the limits of the second derivates for the RHS and LHS are different. One is infinty when the other is 0.

My question is what does this mean exactly? Is the question not possible if my second derivatives are not continuous?
 
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  • #2
First, please tell us what the problem really is! You say "by finding a value of a and b" but tell us nothing about how "a" and "b" are related to the function. Are you given a formula for the function involving a and b? If so, that formula is important information.
 

What is a piecewise function?

A piecewise function is a function that is defined by multiple equations, each of which applies to a different interval of the function's domain.

What does it mean to make a piecewise function continuous?

Making a piecewise function continuous means ensuring that there are no gaps or jumps in the graph of the function. This is done by connecting the different pieces of the function at the points where they meet, in order to create a smooth, continuous curve.

Why is it important to make a piecewise function continuous?

It is important to make a piecewise function continuous because it allows us to accurately represent real-life situations that may involve varying conditions or behaviors. It also allows us to better understand and analyze the behavior of the function.

How do you make a piecewise function continuous using the first derivative?

To make a piecewise function continuous using the first derivative, we need to ensure that the first derivative is continuous at the points where the different pieces of the function meet. This can be done by setting the first derivative of each piece equal to each other at the points of intersection and solving for the unknown variables.

How do you make a piecewise function continuous using the second derivative?

To make a piecewise function continuous using the second derivative, we need to ensure that the second derivative is the same for each piece of the function at the points where they meet. This can be achieved by setting the second derivative of each piece equal to each other at the points of intersection and solving for the unknown variables.

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