A student rewrites the objective function of an optimization problem in terms of a…
MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
A student rewrites the objective function of an optimization problem in terms of a single variable using the given constraint and then solves f′(x)=0 to locate critical points. Which of the following best explains why the student must also evaluate the objective function at the endpoints of the feasible interval for x?
(a) Because the Mean Value Theorem can only be applied once the function values at the endpoints are known.
(b) Checking the endpoints identifies points where the derivative is undefined, which could produce additional extrema.
(c) Absolute extrema on a closed interval can occur either at interior critical points or at the interval endpoints.
(d) The Second Derivative Test requires knowledge of endpoint values to classify critical points.