Consider the function

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

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.