Three claims about critical points and extrema are listed below.
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Three claims about critical points and extrema are listed below.
(1) For Claim A, state whether it is always true. Provide a concise justification based on definitions.
(2) For Claim B, state whether it is always true. If it is false, construct an explicit example of a differentiable function that illustrates the failure and explain thoroughly.
(3) For Claim C, state whether it is always true. If it is true, give an explicit example and explain; if it is false, justify your answer.