Consider the graph of the function f given below (a piecewise linear function that is constant on [−1,1] at height 1, with lines extending beyond).
((a)) Show that f has a local maximum but not a local minimum at the point (−1,1).
((b)) Show that f has a local minimum but not a local maximum at the point (1,1).
((c)) Show that f has a local maximum AND a local minimum at the point (0,1).
((d)) Show that f is constant on the interval [−1,1] and thus has both a local maximum AND a local minimum at every point (x,f(x)) where −1<x<1.