Consider the function y = f(x) shown in the graph below. At points x = 1 and x = 3 determine whether each of the following statements is true of false. Enter your answer in the table below. Y 2 3 x Statement x = 1 x = 3 Left limit exist Right limit exist The limit exist The function is continuous The function is differentiable The derivative f'(x) of a function f(x) defined on [0,3] is shown in the graph below Y 3 X (a) Find the open interval(s) where f is (strictly) increasing, and the open interval(s) where f is (strictly) decreasing. Justify your answer. (b) Find the local maxima and minima of the function f in the open interval (1,3). Is x = 3 a local maximum? Justify your answer. Estimate the area under the graph of f(x) = x above the x-axis and from x = 2 to x = 6 using four approximating rectangles (with the same width, and right endpoints). Sketch the graph of f(x) and of the rectangles on the axes provided. 1 y 12 13 0 4 6 x