Simple Calculus question but I don't understand

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Homework Help Overview

The discussion revolves around a piecewise function defined as f(x) with two expressions depending on the value of x. The original poster is tasked with finding the derivative at a specific point, x = 2, and is confused about the nature of the derivative at that point.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to find the derivative by applying standard differentiation rules to the piece of the function that includes the point of interest. They express confusion about why the derivative is considered undefined, despite calculating a value of 10.
  • One participant suggests using the definition of the derivative, prompting a consideration of limits from both sides of the point in question.
  • Another participant notes that the derivative from the left and right sides yield different results, leading to the conclusion that the derivative is undefined.

Discussion Status

Contextual Notes

Participants are working under the constraints of a homework assignment, which may impose specific rules or expectations regarding the treatment of piecewise functions and their derivatives.

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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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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?
 
ohh. it would equal 1, so 10 doesn't equal 1 so it would be undefined.
 
name_ask17 said:
ohh. it would equal 1, so 10 doesn't equal 1 so it would be undefined.

That's it.
 
Thanks!
 

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