Differentiate heavy side function

In summary, the task is to find points where a given function is differentiable. By drawing a number line and analyzing the given function, it can be observed that the function is not continuous at x=0 and x=2 due to a jump. However, there do not seem to be any other discontinuities in the function. The last note in the conversation may be addressing a possible mistake in the working, where an x was left out in the exponent of f' for x > 2.
  • #1
homo-sapiens
28
0

Homework Statement


find points where function is differentiable
http://puu.sh/cqrc8/f96bd06aee.png

Homework Equations


H(x) = 1, x >= 0
H(x) = 0, x < 0[/B]

The Attempt at a Solution


i Draw a number line and see where the function would change or jump. and immediately i noticed that the function would not be continuous on x=0 and x=2 since that is when the function jumps.
http://puu.sh/cqrBE/44b7fe56ff.png
however i don't see any other discontinuities in the function. if so then what is the last note for? Am i completely missing the point in this question here??[/B]
 
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  • #2
homo-sapiens said:
the function would not be continuous on x=0 and x=2 since that is when the function jumps.
Does it jump at 2? Btw, in your posted working you left out an x in the exponent of f' for x > 2.
 

1. What is the heavy side function?

The heavy side function, also known as the Heaviside step function, is a mathematical function that returns 0 for negative input and 1 for positive input. It is usually denoted by the symbol H(x) or θ(x).

2. How is the heavy side function used in differentiation?

The heavy side function is often used in differentiation to represent a step or sudden change in a function. It can be used to model situations such as a switch turning on or off, or a sudden increase or decrease in a physical quantity.

3. What is the derivative of the heavy side function?

The derivative of the heavy side function is also known as the Dirac delta function. It is defined as 0 for all values except x=0, where it is undefined. The Dirac delta function is often used in physics and engineering to represent a point mass or impulse.

4. How do you graph the heavy side function?

The graph of the heavy side function is a step function that starts at (0,0) and then jumps to (0,1) at x=0. It remains at 1 for all positive x values and 0 for all negative x values.

5. What are the applications of the heavy side function?

The heavy side function has various applications in mathematics, physics, and engineering. It is used to model step functions in differential equations, to represent sudden changes in physical systems, and to define the impulse response in signal processing. It is also useful in analyzing circuit networks and control systems.

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