Question

Which statement about this function is true?
f(x) = |x^2 - 4|

f(x) is continuous and differentiable at x = -2.
f(x) is discontinuous and differentiable x = 2.
f(x) is continuous and non-differentiable at x = -2 and x = 2.
f(x) is discontinuous and non-differentiable at x = -2 and x = 2.

Answer 1

Ok/ so we have, f(x)=|x+2|*|x-2|
This function is continuous, but is not differentiable at x=-2 and x=2, see the left and right hand derivatives will have different signs at those points

Answer 2

Thank you!