Match each function with the correct description of it's differentiability at
x
=
0
\displaystyle {x}={0}
x
=
0
:
-
Not differentiable at x=0 because of a vertical tangent line there.
Not differentiable at x=0 because of a sharp point or cusp there.
Not differentiable at x=0 because of a discontinuity there.
IS differentiable at x=0.
y
=
x
3
\displaystyle {y}={x}^{{3}}
y
=
x
3
-
Not differentiable at x=0 because of a vertical tangent line there.
Not differentiable at x=0 because of a sharp point or cusp there.
Not differentiable at x=0 because of a discontinuity there.
IS differentiable at x=0.
y
=
x
3
\displaystyle {y}={\sqrt[{{3}}]{{{x}}}}
y
=
3
x
-
Not differentiable at x=0 because of a vertical tangent line there.
Not differentiable at x=0 because of a sharp point or cusp there.
Not differentiable at x=0 because of a discontinuity there.
IS differentiable at x=0.
y
=
1
x
\displaystyle {y}={\frac{{{1}}}{{{x}}}}
y
=
x
1
-
Not differentiable at x=0 because of a vertical tangent line there.
Not differentiable at x=0 because of a sharp point or cusp there.
Not differentiable at x=0 because of a discontinuity there.
IS differentiable at x=0.
y
=
∣
x
∣
\displaystyle {y}={\left|{x}\right|}
y
=
∣
x
∣
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