Question

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

Answer 1

The deritive would be a piece wise defined function

Answer 2

how so?

Answer 3

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

Answer 4

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

Answer 5

abs(x) doesn't follow this, consider a simple case

f(x) = abs(x)

Answer 6

hm? what exactally is the wording on your problem?

Answer 7

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