Consider the function

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

h(x)=\ln x + x - 2

, defined for

x>0

. (a) Show that

h(1)<0

and

h(2)>0

. (b) Determine whether the equation

h(x)=0

has a solution on the interval

(1,2)

. Provide a justification based on your work in part (a). (c) Without calculating any derivatives, explain whether

h(x)=0

can have more than one solution on

(1,2)

, and justify your answer.