3. a) Suppose a function y = g(x) satisfies g(0) = 0 and 0 g'(x) 1 for all values of x in the interval 0x3. Explain carefully why the graph of 9 must lie entirely in the triangular region shaded below: y 3 2 2 3 = b) Suppose you learn that g(1) = .5 and g(2) 1. Draw the smallest shaded region in which you can guarantee that the graph of g must lie. 4. Suppose h is differentiable over the interval 0x 3. Suppose h(0) = 0, and that 5h'(x) 1 for 0x1 0 h'(x) .5 for 1x2 -1h'(x) 0 for 2 x3 Draw the smallest shaded region in the x, y-plane in which you can guarantee that the graph of y=h(x) must lie.