Question

Calculus:

Find the derivatives from the left and from the right at x=1 (if they exist). Is the function differentiable at x=1?

f(x) = √(1−x^2)

Answer 1

The left- and right-derivatives are one-sided limits. If the limits exist and are equal, then \(f\) is differentiable.

Answer 2

Basically, you're examining the continuity of the derivative of \(f\).

Answer 3

Do you know if it's DNE?

Answer 4

ás long as you got lim->1 it never reaches 1, so the root is never =0

however 1,01 x 1,01 increases the value, while 0,99 x 0,99 decreases the value. this would indicate conflicting limits and the function is not differentiable at lim x->1