dy dx 1. If y 2 3xy = 18, then at the point H1, 3L is HAL 1 HBL 0 HCL 1 HDL 4 HEL 8 kx + 8 k + x The value of k is

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1 . If = 8, then d d at the point H, L is 0 HCL HDL HEL 8. The equation of the line tangent to the curve = k + 8 k + The value of k is at = is = +. HCL HDL HEL. If f HL = and f H L =, then find f HL d 0 HCL 9 HDL 6 HEL. The figure below shows the graph of the acceleration of an object moving on the ais as a function of time. Assume that v H0L = 0. Among the marked points, which time corresponds to the greatest speed of the object? ahtl B A C t ahtl D E A B HCL C HDL D HEL E. Find lim HCL HDL HEL Does not eist 6. If = f H L and f HL = è!!!!!!!!!!!!!!! then d d is equal to è!!!!!!!!!!!!!!!!! 9 è!!!!!!!!!!!!!!!!! HCL è!!!!!!!!!!!!!!!!! 9 HDL è!!!!!!!!!!!!!!!!! HEL 8 è!!!!!!!!!!!!!!!!! 9 7. Determine which of the following is not true for f HL = a, a > f H0L = f HL = 0 HCL lim f HL = 0 HDL lim f HL = HEL lim f HL = 8. If f HL = + 8, and g HL is the inverse function of f, then g H0L is equal to HCL HDL HEL Not enough information to determine g H0L

2 9. Suppose that f and g are continuous functions, and that f HL d = 0, g HL d =, f HL d =, and g HL d = 8, then find H f HL g HLL d 8 HCL HDL 6 HEL Not enough information is given 0. Suppose f HL = è!!!!!!!!!!!! 9. On an interval where the inverse function = f HL eists, find d d Hf HLL 9 HCL HDL è!!!!!!!!!!!! 9 HEL è!!!!!!!!!!!! 9. Solutions of the differential equation whose slope field is shown below are most likel to be quadratic cubic HCL sinusoidal HDL eponential HEL logarithmic. The table below shows some of the values of f HL : 0 f HL 7 f HL could be a linear function a quadratic function HCL a cubic function HDL a fourth degree function HEL a logarithmic function

3 . Consider the table of values for f HL and f HL 0 f HL f HL 0 6 Find the average value of f HL on the D 0 HCL HDL HEL Cannot be determined from the information given. Suppose that f HL < 0 throughout the domain of a given function. If we are given f HL, an initial value, and asked to use Euler s Method to approimate a solution, then Euler s Method will underapproimate the solution Euler s Method will overapproimate the solution HCL Euler s Method will underapproimate the solution for all > 0, overapproimate for all 0 HDL Euler s Method will overapproimate the solution for all > 0, underapproimate for all 0 HEL Not enough information is given to make this determination. A rectangle is to be inscribed within the parabola = 8 6, with one side ling on the ais, and two vertices ling on the curve Hsee diagraml. Find the maimum possible area of the rectangle = HCL HDL 0 HEL 8 6. Evaluate sec tan d è!!! HCL 8 è!!! HDL è!!! HEL è!!! 7. Find the approimation of the area under the curve = + on the D using the Trapezoidal Rule with n =. 8 HCL 8 HDL 0 HEL 6

4 Consider the following piecewise defined functions defined below to answer problems 8 and 9 below ghl fhl 8. If h HL = f HL g HL, find h HL 0 HCL HDL HEL Does not eist 9. If k HL = g HL f HL, find k H L 7 8 HCL HDL HEL 0. Suppose f HL = 6 +. Find all values where inflection points occur = 0 =, HCL = 0,, HDL = 0, è!!!, è!!! HEL No inflection points. Find the area bounded b the curves = and = HCL HDL 8 HEL 9. If =, find H L 8 + H L HCL HDL 8 H L H L HEL H L. Evaluate 0 e H e L d ln He L HCL e H el HDL e HEL e e

5 . Suppose that the derivative of f has the graph as shown below f HL Which of the following could be the graph of f? HCL HDL HEL n. Find lim n k = sin i k j k z J n { n N 6. Evaluate lim HCL HDL HEL cot H L cot 0 HCL HDL è!!! HEL 7. Find the value of c for which the function f HL = + c has a local minimum at =. 8 HCL HDL HEL

6 8. A man tall walks at the rate of toward a streetlight that s above the ground. Find the rate at which the tip of his shadow is moving Hin relation to the light polel. HCL 0 HDL 8 HEL 8 9. Consider the graph below of f HL. Let G HL = f HtL dt and H HL = f HtL dt. Which of the statements below is true? 0 f fhl t G HL = H HL G HL = H H + L HCL G HL = H H + L HDL G HL = H HL HEL G HL = H HL + 0. cos d = sin + cos + C sin cos + C HCL sin + C HDL sin + C HEL sin + sin + C