MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A function f is continuous on [0,3], differentiable on (0,3), and satisfies the derivative bound
∣f′(x)∣≤4for 0≤x≤3.
In addition, f(0)=2.
(1) Obtain the largest possible value of ∣f(3)−2∣. Show all reasoning leading to your conclusion.
(2) Using part (a), describe the entire interval of values that f(3) can attain.
(3) An experimental measurement gives f(3)=9. Discuss whether this measurement is compatible with the derivative bound and the given initial value. Support your conclusion with reasoning or calculation.