Let be twice-differentiable on an interval containing with
MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Let g be twice-differentiable on an interval containing x=4 with g′′(4)<0. A student uses the tangent line at x=4 to approximate g(4.2). Which statement about the accuracy of the student’s approximation is true?
(a) The approximation is an underestimate because g is concave down at x=4.
(b) The approximation could be either an overestimate or an underestimate; more information is needed.
(c) The approximation is an overestimate because g is concave down at x=4.
(d) The approximation is an overestimate because g′(4) is positive.