For each of the following problems, draw a graph with the given requirements. (a) Draw a graph f on [0, 1), such that f(r) is positive, f'(r) is negative, and f"(I) is positive. (b) Draw a graph f on [0, 1), such that f(z) is negative, f'(1) is negative, and f"(r) is negative. (c) Draw a graph f on [0, 1), such that f'(z) is negative, and f"(z) is zero. (d) Draw a graph f on [0, 1), such that f(r) is negative, f'(r) is positive, and f"(x) is positive. (c) Draw a graph f on [0, 1), such that f(r) is positive, f'(r) is positive, and f"(r) is negative. (f) Draw a graph f on (0, 1), such that f'(2) is positive, and f"(r) is zero