Sketch a neat graph of a function with domain [0,4] that clearly has the required properties in each case, without the graph containing a straight line on any significant interval:

(a) f(x) is increasing and concave on [0,1], increasing and convex on [1,2], and has a global minimum at x = 3.

(b) g(x) is convex on [0,1], convex on [1,3], and has global maxima at x = 1, x = 3 and x = 4.

(c) h(x) is convex on [0, 1], concave on [1, 2], convex on [2, 4], and has no stationary points.