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.
a. Obtain the largest possible value of ∣f(3)−2∣. Show all reasoning leading to your conclusion.
b. Using part (a), describe the entire interval of values that f(3) can attain.
c. 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.