F (x) = |x - 1| find the derivative from the left at x = 1. if it does not exist, enter none.

Question

Mathematics

Carl Sutton

20 November, 13:03

F (x) = |x - 1| find the derivative from the left at x = 1. if it does not exist, enter none.

+3

Answers (1)

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Camila · Answer 1

Given: f (x) = |x - 1|

A graph of the function is shown below.

The function is either

f (x) = x-1, for x>1

or

f (x) = 1-x, for x<1

Therefore

f' (x) = 1, for x>1

and

f' (x) = - 1, for x<1

Answer: - 1