Mathematics

Problem

Let

h(x)=(x-1)^{1/3}+2

. Which statement correctly characterizes

h'(x)

x\to 1

? a)

h'(x)\to 0

, so the tangent line is horizontal at

x=1

. b)

h'(x)

approaches a finite non-zero constant equal to

\tfrac13

. c)

h'(x)

grows without bound, indicating a vertical tangent at

x=1

. d)

h'(x)\to -\infty

, showing a vertical tangent slanted downward at

x=1