AP Calculus ABmediummcq1 pt

Which of the following functions has a vertical tangent line at x=0x=0?

A.f(x)=xf(x)=|x|
B.f(x)=x2f(x)=x^2
C.f(x)=x1/3f(x)=x^{1/3}
D.f(x)=1xf(x)=\dfrac{1}{x}

Explanation

Core Concept

Its derivative is 13x2/3\dfrac{1}{3}x^{-2/3}, which grows without bound as x0x\to 0. The tangent line at 00 is vertical.

Correct Answer

Cf(x)=x1/3f(x)=x^{1/3}

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