The relation defines implicitly as a differentiable function of on where

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

Problem

The relation

x^{2}+y^{2}=25

defines

y

implicitly as a differentiable function of

x

(-5,5)

where

y>0

. Which statement about the concavity of the graph of this function on

(-5,5)

is true? (a) The graph is concave down on

(-5,0)

and concave up on

(0,5)

. (b) The graph is concave down on the entire interval. (c) The graph is concave up on the entire interval. (d) The graph changes concavity at

x=\pm\sqrt{12.5}