A student writes: “Because the function is continuous on and differentiable on
MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A student writes: “Because the function g is continuous on [1,5) and differentiable on (1,5), the Extreme Value Theorem ensures that g has both a maximum and a minimum value on [1,5).”
Identify the specific hypothesis of the theorem that is violated in the student’s statement and state the correct conclusion about g that can (or cannot) be made from the given information.