1.Given f '(x) = (x + 1)(6 + 3x), find the x-coordinate for the relative minimum on the graph of f(x). (5 points)0-1-2None of these2.Use the graph of f '(x) below to find the x values of the relative maximum on the graph of f(x): (5 points)0.5211.53.Given the position function s(t), s(t) = t3 + 4t, where s is measured in meters and t is in seconds, find the velocity and acceleration of the particle at t = 2 seconds. (5 points)8 m/sec; 4 m/sec210 m/sec; 3 m/sec216 m/sec; 16 m/sec216 m/sec; 12 m/sec24.Given the position function, , between t = 0 and t = 9, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right. (5 points)3 < t < 95 < t < 9The particle never moves to the right.The particle always moves to the right.5.Given the relationship x3 + 2y2 =10, with y > 0 and = 4 units/min., find the value of at the instant y = 1 unit. (5 points) units/min units/min units/min units/min6.The base of a triangle is decreasing at the rate of 1 ft/sec, while the height is increasing at the rate of 2 ft/sec. At what rate is the area of the triangle changing when the base is 10 ft and the height is 70 ft? Remember to use the product rule when you find the expression for . (5 points)-25 ft2/sec-45 ft2/sec-50 ft2/sec45 ft2/sec7.Find . (5 points)108.Evaluate . (5 points)07-∞∞9.Which of the following statements is/are true? (5 points)I. If f '(x) exists and is nonzero for all x, then f(1) ≠ f(0). II. If f is differentiable for all x and f (-1) = f(1), then there is a number c, such that |c| < 1 and f '(c) = 0. III. If f '(c) = 0, then f has a local maximum or minimum at x = c.I onlyII onlyI and III onlyI and II only10.The local linear approximation of a function f will always be less than or equal to the function's value if, for all x in an interval containing the point of tangency, (5 points)f ' < 0f ' > 0f " < 0f " > 01.Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 6x(1/3) + 3x(4/3). You must justify your answer using an analysis of f '(x) and f "(x).2.What is the maximum volume in cubic inches of an open box to be made from a 16-inch by 30-inch piece of cardboard by cutting out squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative. Give one decimal place in your final answer.3.The position function of a particle in rectilinear motion is given by s(t) = t3 - 12t2 + 45t + 4 for t ≥ 0 with t measured in seconds and s(t) measured in feet. Find the position and acceleration of the particle at the instant when the particle reverses direction. Include units in your answer.4.A circle is growing so that the radius is increasing at the rate of 3 cm/min. How fast is the area of the circle changing at the instant the radius is 12 cm? Include units in your answer.5.The side of a square is measured to be 12 ft with a possible error of ±0.1 ft. Use linear approximation or differentials to estimate the error in the calculated area. Include units in your answer.

1) Find x to the nearest degree if x = sin-1 (2/3)a. 1°b. 42°c. 48°d. 73°2) Find x to the nearest degree if x = arctan 0.a. 270°b. 90°c. 45°d. 0° 3) Find x in radians if x = arccos (¼). Round to the nearest hundredth.a. 1.32b. 75.52c. 0.97d. 1.004) Find x in radians if x = sin-1(5/8). Round to the nearest hundredth.a. 0.01b. 38.7c. 0.68d. 0.595) Find the value of the expression below. Round to the nearest hundredth.a. 88.3b. 0.66c. 1.51d. 57.36) Find the value of the expression below. Round to the nearest tenth.a. 0.76b. 1.00 c. 0.63d. 1.597) Find the value of the expression below. Round to the nearest hundredth.tan(Arctan 4)a. 75.96b. 4c. 0.00d. 89.258) Simplify [cos(arc cos x)] • [(Arc sin(sin y)]A. x/y B x2y2C. xyD. x9) The cruise ship Reno sailed due West 24 miles before turning south. When the Reno became disabled and radioed for help, the rescue boat found that the fastest route to her covered a distance of 48 miles. The cosine of the angle at which the rescue boat should sail is 0.5. Find the angle Θ, nearest tenth of a degree, at which the rescue boat should travel to aid the Reno.a. 26.6°b. 30°c. 60°d. 87.3°10) To the nearest degree, what is the angle of depression Θ between the shallow end and the deep end of the swimming pool shown below?a. 25°b. 37°c. 53°d. 73°

Question 1:A researcher is interested in knowing if there are differences between the incidence of accidents among (1) employees who received only video safety training and (2) employees who received hands-on safety training.They were able to collect 102 responses from a random number of employees. Among them, 27 video-only employees were in accidents, 36 were not; 23 hands-on training were in accidents, 16 were not. Construct a contingency table. Run the Chi-Square test for independence using the calculator in the Module. State your findings and their significance. Do not forget to give summary statistics in APA format.Question 2:A researcher has found that pilots taking an over the counter antihistamine have poor reaction times. They performed an experiment on 22 pilots: 11 took the medication and 11 did not. Their reaction times to a command by Air Traffic Control was considered to be adequate or inadequate. Among those taking the medication, 9 were rated inadequate and 2 adequate. Among those not taking the medication, 10 were rated adequate and only 1 inadequate. Construct a contingency table. Run the Chi-Square test for independence using the calculator in the module. Construct a contingency table.•State your findings and their significance. Do not forget to give summary statistics in APA format.•What is the problem with this research study? Is the Chi-Square test appropriate? Why or why not? What could the researcher do to potentially rectify the problem?