Mathematics

Mathematics

Problem

Consider the function

g(x)=\dfrac{x}{x-1},\; x\ne1

. Which statement about the concavity of

g

is true? a)

g

is concave up for

x<1

and concave down for

x>1

; it has no points of inflection. b)

g

is concave down for

x<1

and concave up for

x>1

; it has a point of inflection at

x=1

. c)

g

is concave down for

x<1

and concave up for

x>1

; it has no points of inflection. d)

g

is concave up for all

x\neq 1

; it has no points of inflection.

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