Define the function h(x)= cases x^ 2 -4 x-2 , & x 2, , & x=2

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Define the function

h(x)=\begin{cases}\dfrac{x^{2}-4}{x-2}, & x\neq 2,\\k, & x=2.\end{cases}

For which value of

k

does

h'(2)

exist? (a)

k=1

(b)

k=4

(c)

k=2

(d) No value of

k

makes

h'(2)

exist

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