Define the piecewise function
q(x)=⎩⎨⎧x−2x2−4,k,x=2,x=2,
where k is a constant to be chosen. Consider the closed interval [0,4].
a. Part 1: (a) Determine the value of k that makes q continuous at x=2. Show your work.
b. Part 2: (b) Verify that, with your chosen value of k, all hypotheses of the Extreme Value Theorem are satisfied for q on [0,4].
c. Part 3: (c) Find the absolute maximum and absolute minimum values of q on [0,4] and the corresponding x-values where they occur. Justify your answer by analyzing critical points and endpoints.