Question

Find the derivative of f(x)=|x^2-1| at the point (1, 0)

-1
0
1
Does not exist

Answer 1

Does not exist.

Explanation:

d/dx |u| = (u / |u|) * du/dx

Here u = x^2 - 1 and du/dx = 2x , so we have

2x (x^2 - 1) / |x^2 - 1| as the required derivative.

At the point (1,0)

the denominator = |1^2 - 1| = 0

- so the derivative does not exist at (1, 0)