The differential equation has a solution passing through
MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
The differential equation dxdy=y−x2 has a solution passing through (0,1). A single tangent-line step of length 0.2 is taken from x=0 to approximate the value of y(0.2). Based on concavity considerations, which statement about the approximation is correct?
(a) The approximation is greater than the actual value because the curve is concave up near x=0.
(b) The approximation equals the actual value because the differential equation is linear near x=0.
(c) The approximation is less than the actual value because the curve is concave up near x=0.
(d) The approximation is greater than the actual value because the curve is concave down near x=0.