Simple Calculus question but I don't understand

[name_ask17]

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.

 

[Dick]

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?

 

[name_ask17]

ohh. it would equal 1, so 10 doesn't equal 1 so it would be undefined.

 

[Dick]

ohh. it would equal 1, so 10 doesn't equal 1 so it would be undefined.

That's it.

 

[name_ask17]

Thanks!