The function is defined on the interval

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

Problem

The function p(x)=xp(x)=\sqrt{x} is defined on the interval [0,4][0,4]. Which of the following describes p′(0)p'(0)? (a) p′(0)=0p'(0)=0 (b) p′(0)p'(0) does not exist because lim⁡x→0+x−0x−0\displaystyle \lim_{x\to 0^{+}} \dfrac{\sqrt{x}-0}{x-0} is unbounded. (c) p′(0)=∞p'(0)=\infty (d) p′(0)p'(0) does not exist because pp is not defined for x<0x<0

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