If , then at ,…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

If f(x)={x(e4/x−e−4/xe4/x+e−4/x),x≠00,x=0f(x)=\begin{cases}x\left(\frac{e^{4/x}-e^{-4/x}}{e^{4/x}+e^{-4/x}}\right),&x\ne0\\0,&x=0\end{cases}, then at x=0x=0, f(x)f(x) is (1) Differentiable (2) Not differentiable (3) f′(0)=−1f'(0)=-1 (4) f′(0)=1f'(0)=1

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