Find the Derivative of the given Function

In summary, the conversation involved sketching the derivative of a given function and finding the derivative of the function. The derivative was described as starting at the origin, sloping down vertically, continuing horizontally, then going back up the x-axis and continuing horizontally. It was then discussed that the graph of the derivative of the slopey part would be three horizontal lines at levels 0, minus-something, and 0 again. The final response was a thank you for the help.
  • #1
apcalckid76
3
0
1.Sketch the Derivatie of the given Function



2. Help me find the derivative of the function



3. I said that the derivative will begin at the origin, then slope down vertically, then continute shortly horizontally, then go back up the "X" axis and continue horizonally.

http://imageshack.us/a/img717/7821/img20121020142636.jpg [Broken]

Homework Statement



THanksss

Homework Equations





The Attempt at a Solution

 

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  • #2
welcome to pf!

hi apcalckid76! welcome to pf! :smile:
apcalckid76 said:
3. I said that the derivative will begin at the origin, then slope down vertically, then continute shortly horizontally, then go back up the "X" axis and continue horizonally.

nooo

try this part …

what does the graph of the derivative of just the slopey part in the middle look like?​
 
  • #3
http://imageshack.us/a/img10/5516/img20121021084205.jpg [Broken]



This is my answer...my physics teacher helped me solve it but I am not sure if its right or not.
 
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  • #4
yes, that's right :smile:

the three parts of the original graph are straight,

so that means their derivatives (= the slopes) are constant,

so the graph of the derivative is three horizontal lines, at levels 0 minus-something and 0 again :wink:







:
 
  • #5
THANK YOU! I really appreciate it Tim thanks!
 

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a given point. It is the slope of the tangent line at that point on the function's graph.

How do I find the derivative of a function?

To find the derivative of a function, you can use the derivative rules, such as the power rule, product rule, quotient rule, and chain rule. These rules help determine the derivative of a function based on its algebraic form.

Why is finding the derivative important?

The derivative is important because it helps us understand the behavior of a function at a specific point. It can also be used to find the maximum and minimum values of a function, as well as the function's increasing and decreasing intervals. In addition, derivatives are essential in fields such as physics, economics, and engineering.

Can I find the derivative of any function?

Yes, you can find the derivative of any function, as long as it is a continuous function. However, some functions may require more advanced techniques, such as implicit differentiation, to find the derivative.

How can I check if my derivative is correct?

To check if your derivative is correct, you can use the derivative rules to simplify the expression and see if it matches the original function. You can also use graphing tools to plot both the function and its derivative and see if they align. Additionally, you can use the second derivative to verify that the first derivative is correct.

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