Consider the upper semicircle defined implicitly by with

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Consider the upper semicircle defined implicitly by

x^{2}+y^{2}=4

with

y>0

. Which statement about its concavity with respect to the

x

–axis is correct? (a) The curve is concave down when

x<0

and concave up when

x>0

, with an inflection point at

x=0

. (b) The curve is concave down for all

x

and has no inflection points. (c) The curve is concave up for

|x|<\sqrt{2}

and concave down for

|x|>\sqrt{2}

, with inflection points at

x=\pm\sqrt{2}

. (d) The curve is concave up for all

x

and has no inflection points.