would the derivative of f(x) = 4 - abs(x) be DNE?

Question

anonymous · Answer

The deritive would be a piece wise defined function

anonymous · Answer

how so?

anonymous · Answer

When you take a derivative of a function you need to look at derivatives coming from the left and the right.

anonymous · Answer

because the problem that I'm doing requires me to plug in a extremum after finding the derivative

anonymous · Answer

abs(x) doesn't follow this, consider a simple case

f(x) = abs(x)

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anonymous · Answer

hm? what exactally is the wording on your problem?

anonymous · Answer

find the value of the derivative (if it exists) at each indicated extremum
and the problem is f(x) = 4 - abs(x) with the point (0,4) given as the max so that it looks something like this

anonymous · Answer

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