Define the piecewise function p(x)=⎩⎨⎧x−1x2−4,0,x=1,x=1.
Consider the closed interval [−2,4].
a. Part 1: (a) Show that p is continuous on [−2,4].
b. Part 2: (b) Compute p′′(x) for x=1 and simplify your result.
c. Part 3: (c) Determine all x in [−2,4] at which p′′(x)=0 or p′′(x) is undefined.
d. Part 4: (d) Create a complete sign chart for p′′ on [−2,4] and hence determine the intervals on which the graph of p is concave up and concave down.
e. Part 5: (e) State the x-coordinates of any points of inflection of p on [−2,4] and justify each using your work above.