m0x+bg ingxgl E[x)= m1x+b1 if1

mox + bo mlX + bl m2X -F b2 if 2 < x < 3 Note that the function has 3 different pieces, and each piece is a straight line. We will want this function to satisfy the following properties: E(x) is continuous on the interval [O, 31. In particular, it is continuous at x = 1 and x = 2, and The slope of the line over the interval (n, n + 1) should be f '(n), similar to how we use derivatives as slopes for linear approximation functions. Once we have constructed E(x), we can use it to estimate f (3) E(3). To construct E(x), we need to find appropriate values for the constants mo, mi, m-2, bo, bl. b2. Complete the following steps to find these values. a) (6 points) The constants mo. mi, m2 are the slopes of the three different pieces of E(x). The slope over the interval (n, n + 1) should be f '(n). Use this relation for n = O, n = 1, and n = 2 to find the values for mo, and b) (3 points) The constant bo should be chosen so that E(O) value for bo. = f(0). Use the given value of f (O) to find the correct