The derivative of a twice-differentiable function has a relative maximum at
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The derivative f′ of a twice-differentiable function f has a relative maximum at x=5. Which statement about the graph of f at x=5 is most accurate?
(a) f has a relative maximum at x=5 because f′ changes from positive to negative there.
(b) f has a horizontal tangent at x=5 since f′(5)=0.},{
(c) f has a point of inflection at x=5 because f′′(5)=0 and its concavity changes.
(d) f is concave down on both sides of x=5 because f′′(5)=0 and f′ is decreasing there.