Let
f(x)={x2−4x+3,x+1,0≤x<2,2≤x≤5.
The domain of interest is the interval [0,5].
a. Part 1: (a) Identify and classify the discontinuity of f at x=2. Provide a brief justification.
b. Part 2: (b) Determine whether the Extreme Value Theorem applies to f on [0,5]. Give a reasoned explanation.
c. Part 3: (c) Find a subinterval of [0,5] on which the Extreme Value Theorem does apply to f. State the interval and justify your choice.
d. Part 4: (d) On the original interval [0,5], compute the absolute maximum and minimum values of f (if they exist) and the x-values at which they occur. Discuss how your findings relate to your conclusion in part (b).