A student writes the following justification: “Since is continuous on
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A student writes the following justification:
“Since q(x)=∣x∣ is continuous on (−2,5], the Extreme Value Theorem guarantees that q attains both an absolute maximum and an absolute minimum on this interval.”
Which of the following identifies the flaw in the student’s reasoning?
(a) The interval (−2,5] is not closed, so one of the theorem’s hypotheses is violated.
(b) q is not differentiable at x=0, so the theorem cannot be applied.
(c) The function is not continuous at x=−2, so the theorem cannot be applied.
(d) The function must be monotonic on the interval for the theorem to apply.