Simple Calculus question but I don't understand

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In summary, the conversation discusses finding the derivative of a piecewise function, f(x), where the function is defined differently for x values less than or equal to 2 and x values greater than 2. The individual has attempted to find f'(2) by taking the derivative of the top equation, but got an answer of 10 instead of the expected answer of undefined. After a discussion on the definition of derivative and the limit as h approaches 0, it is determined that f'(2) is undefined due to the different results obtained when h is positive and negative, making the function discontinuous at x=2.
  • #1
name_ask17
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Homework Statement



f(x)= {x^3 - 2x, x<=2
x + 2, x> 2

find f'(2)


Homework Equations


Ok, i tried by taking the derivative of the top equation, since it includes 2, but I got the answer to be 10.


The Attempt at a Solution



By book says the answer is undefined, but I don't understand why. Thsi is under "quick review" so I'm thinking I'm making it a lot harder than it should be. Am I missing something? Why is it undefined? I keep getting 10.
 
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  • #2
Remember the definition of derivative. f'(2) is the limit as h->0 (f(2+h)-f(2))/h. If h is negative and approaching zero, then sure, you get 10. But what about if h is positive and approaching zero?
 
  • #3
ohh. it would equal 1, so 10 doesn't equal 1 so it would be undefined.
 
  • #4
name_ask17 said:
ohh. it would equal 1, so 10 doesn't equal 1 so it would be undefined.

That's it.
 
  • #5
Thanks!
 

1. What is calculus?

Calculus is a branch of mathematics that deals with the study of change and motion. It involves the analysis of functions and their rates of change, and is essential for understanding many scientific and engineering principles.

2. What are the basic concepts of calculus?

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