Which function is not differentiable at x = 0?
- f(x) = x²
- f(x) = |x|
- f(x) = sin(x)
- f(x) = eˣ
Explanation
f(x) = |x| has a cusp at x = 0, making it non-differentiable there.
A function is differentiable at a point if its derivative exists at that point.
The absolute value function, (f(x)=|x|), has a sharp corner at (x=0).
Functions with sharp corners are not differentiable at those points.
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