2:07 PM Tue 2 Jun * 50% Question 1 Given the function f(x) = 2x² –-x-1 (a) Is the point (-1, 2) on the graph of f . (b) If x =-2, what is f(x)? What point is on the graph of f ? (c) If f(x)=-1, what is x ? What point(s) are on the graph of f ? (d) What is the domain of f ? (e) List the x - intercepts, if any, of the graph of f. (f) List the y - intercepts, if there is any, of the graph of f. (g) Find all point(s) at which f'(x)=0? (h) Determine the intervals on which the graph of f(x) is increasing and the intervals on which it is decreasing. (i) Use the First Derivative Test to identify the maximum and/or minimum point(s) of f(x). (j) Use the Second Derivative Test to determine the nature of concavity of f(x). (a) Consider the piecewise function -x+1, if x<1 f(x) ={x-1, if 1 2 (i) Find lim f(x) if it exists. * >1 (ii) Show that f(x) is continuous at x= 2. (iii) Sketch the graph of f(x). dy (b) Use the techniques of differentiation to find dx (i) 3e* = xy+ x² + y² 2x (ii) у%3D (* 4)° (c) Find the slope of the tangent line at the indicated point y' +y = x at (1,3) Write an equation of the tangent line. (d). Let f(x) %— х* +х-1. (i) Use the Intermediate Value Theorem to show that f (x) has at least one root in the interval [О, 1]. (ii) Starting at x, = 1, use the Newtons method to approximate this root.