Consider the piecewise function
f(x)=⎩⎨⎧x+21,sin(πx),−2<x≤0,0<x≤1.
Answer the following questions about f on the intervals shown.
a. Part 1: Determine whether the hypotheses of the Extreme Value Theorem are satisfied on the interval [−2,1]. Justify your conclusion carefully.
b. Part 2: Determine whether the hypotheses of the Extreme Value Theorem are satisfied on the interval (−2,1]. Justify your conclusion carefully.
c. Part 3: For the interval in part (a), identify all points at which f attains an absolute maximum or an absolute minimum, and state the corresponding extremum values.
d. Part 4: Explain why any absolute extremum identified in part (c) must occur either at an endpoint of the interval or at a critical point of f.