1.Use the graph of f(x) below to estimate the value of f '(-2): (4 points)-10142.Given the graph of f '(x), the derivative of f(x), which of the following statements are true about the graph of f(x)? (4 points)I. The graph of f has a critical point at x = 0. II. The graph of f has a critical point at x = 1. III. The graph of f has a point of inflection at x = 1.I onlyII onlyIII onlyI and III only3.Find the critical point of the function f(x) = x2 - 2x + 7. (4 points)(-1, 10)(-1, 6)(1, 0)(1, 6)4.For what values of x is the graph of concave upward? (4 points)No values of xx < 6x > -6x > 65.At what value(s) of x does f(x) = x4 - 18x2 have a critical point where the graph changes from decreasing to increasing?(4 points)0 and -3 only0 and 3 only-3, and 3 only0 only1.The maximum value of f(x) = 2x3 - 18x2 + 48x - 1 on the interval [0, 3] is (4 points)-13935712.In which interval is the function f(x) = - 4x2 + 12x + 1 increasing? (4 points)(-∞, 2) only(-∞, 2) U (6, ∞)(6, ∞) only(2, 6) only3.What are the critical values on the graph of y = x4 + 6x2 - 5? (4 points)x = -1 and 1x = -3, 0, and 3x = 0There are no critical values for this function.4.Find the x-coordinate of the point(s) of inflection on the graph of y = x3 - 12x2 - 5. (4 points)x = -2x = 4x = 2x = 125.Which one of the following statements is true? (4 points)If f ′′(x) > 0 on the interval (a, b), then f is concave up on the interval (a, b).If f ''(c) = 0, then x = c is an inflection point on the graph of f(x).If f is continuous on a closed interval [a, b], then f attains an absolute maximum value and f attains an absolute minimum inside the interval [a, b].None of these are true.1.Find the absolute maximum value of the function . (4 points)0412None of these2.In the answer space below, provide one of the two positive integers whose product is 196 and whose sum is a minimum. (4 points) 3.A farmer has 1,800 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. Write the function that will produce the largest area if x is the short side of the rectangle. (4 points)f(x) = -2x2 + 1800xf(x) = -x2 + 1800xf(x) = x2 - 1800f(x) = 2x2 - 18004.What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 12 - x2? (4 points)81216325.If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000. (4 points)1.A particle moves with velocity function v(t) = - t2 + 5t - 3, with v measured in feet per second and t measured in seconds. Find the acceleration of the particle at time t = 3 seconds. (4 points) feet per second2-1 feet per second2-3 feet per second26 feet per second22.A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t) = (t)In(2t). Find the acceleration of the particle when the velocity is first zero. (4 points)2e22eeNone of these3.The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 50t - 2t2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop? (4 points)12.5 sec10 sec15 sec60 sec4.The position of a particle on the x-axis at time t, t > 0, is s(t) = ln(t) with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for e ≤ t ≤ 2e? (4 points)ln25.A particle moves along the x-axis so that at any time t, measured in seconds, its position is given by s(t) = 4sin(t) - cos(2t), measured in feet. What is the acceleration of the particle at time t = 0 seconds? (4 points) 1.If y = 2x3 - 4x and , find when x = 1. Give only the numerical answer. For example, if = 3, type only 3. (4 points) 2.The area A = πr2 of a circular oil spill changes with the radius. At what rate does the area change with respect to the radius when r = 3ft? (4 points)6π ft2/ft3π ft2/ft6 ft2/ft9π ft2/ft3.A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by V = x2h cm3. Find the rate at which the volume of the box is changing when the edge length of the base is 4 cm, the edge length of the base is increasing at a rate of 2 cm/min, the height of the box is 15 cm, and the height is decreasing at a rate of 3 cm/min. (4 points)The volume of the box is decreasing at a rate of 192 cm3/min.The volume of the box is increasing at a rate of 288 cm3/min.The volume of the box is decreasing at a rate of 288 cm3/min.The volume of the box is increasing at a rate of 192 cm3/min.4.The height of a cylinder with a fixed radius of 6 cm is increasing at the rate of 3 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is 20cm. (4 points)36π108π360πNone of these5.A 10-ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/sec, how fast, in ft/sec, is the top of the ladder sliding down the wall, at the instant when the bottom of the ladder is 6 ft from the wall? Answer with 2 decimal places. Type your answer in the space below. If your answer is a number less than 1, place a leading "0" before the decimal point (ex: 0.35). (4 points)

Question 1 2 ptsMonika wants to measure the amount of money that different graduate school students spend on fast food (measured in dollars). She selects 20 random graduate students at CSUN, 20 random graduate students at UCLA, and 20 random graduate students from USC. She then measures the total amount of money each student spends on fast food at the end of one week. She wants to see (overall) if the amount of money spent by students is significantly different across the different schools. Which type of analysis is appropriate to test for this?Group of answer choicesFactorial ANOVAOne-way ANOVATukey HSD testScheffe adjustmentQuestion 2 2 ptsJohn conducts a one-way ANOVA to compare 4 different groups (using an a = 0.05) and finds that they are significantly different from each other. He is interested in seeing which groups are significantly different from each other, so he conducts a Tukey HSD post-hoc test afterwards (using a = 0.05). However, he wants to make sure that his total Type I error for the one-way ANOVA and the post-hoc test is only 5% (not 10%). Using a Bonferroni adjustment, what would his new alpha level be?Group of answer choices0.010.01250.0250.017Question 3 2 ptsYou design a study to be a 2 x 3 Factorial ANOVA. Choose the correct amount of independent variables and levels in each independent variableGroup of answer choices2 independent variables, 6 levels in the 1st independent variable, 6 levels in the 2nd independent variable3 independent variables, 2 levels in the 1st independent variable, 2 levels in the 2nd independent variable2 independent variables, 2 levels in the 1st independent variable, 3 levels in the 2nd independent variable3 independent variables, 3 levels in the 1st independent variable, 3 levels in the 2nd independent variableQuestion 4 2 ptsIn a one-way ANOVA, the Within Groups Error we calculate is based on the difference of each individual's DV score from their group's mean. Group of answer choicesTrueFalseQuestion 5 2 ptsWhen you only have two different categorical groups in your IV, performing a dependent samples t-test and a one-way ANOVA will result in the exact same p-value.Group of answer choicesTrueFalseQuestion 6 4 ptsYou run four different one-way ANOVAs. You would like to reduce your Type I error (because after these 4 tests, your Type I error chance is ~20%)! Based on the number of tests you ran, you determine that you need to lower your alpha level to 0.0125 for each ANOVA. If each ANOVA has 3 groups in it (a = 3) and each group has 16 participants (s = 16), what is your new critical F value with this lower alpha level?(Round your answer to two decimal places)Question 7 4 ptsAfter conducting a one-way ANOVA, you find that there are significant differences across four different groups. Each group has an equal number of people in it, so you decide to follow this one-way ANOVA with a Scheffe adjustment to see which of these groups are significantly different from each other. You calculate the final Scheffe value to be 3.256. Based on the means of each group (below), identify ALL of the following groups that are significantly different from each other...Group 1: 5.248 Group 2: 7.589 Group 3: 8.562 Group 4: 3.123Group of answer choicesGroup 2 vs. Group 4 Group 3 vs. Group 4Group 1 vs. Group 3 Group 2 vs. Group 4 Group 3 vs. Group 4Group 1 vs. Group 2 Group 2 vs. Group 3 Group 1 vs. Group 4Group 1 vs. Group 3Group 2 vs. Group 3Question 8 2 ptsTo do a 2x2 factorial ANOVA by hand, you need to have way too much time on your hands, a lot of formulas written down, and a lot of practice (especially for exam 3). (Choose answer "Yes" below -- it is the correct answer)Group of answer choicesNoMaybeYesI don't know!Question 9 6 ptsGiven the data for a one-way ANOVA (below), calculate the Sums of Squares Between Groups. Round your answer to two decimal points. ParticipantGroup 1Group 2Group 3S120 22 18 S212 20 40 S316 19 10 S416 24 20 (Hint: start by finding the means for the groups...)Question 10 4 ptsThe following Summary Table is incomplete. For this one-way ANOVA, find the missing F value. Source Sums of Squares Degrees of Freedom Mean Square F Between Groups 420 2 Within Groups Total 1764 23 Group of answer choices2104.310.302.733.28Question 11 4 ptsGiven the following summary table for a one-way ANOVA, calculate an Omega Squared effect size estimate:Source Sums of Squares Degrees of Freedom Mean Square F Between Groups 12.56 4 3.14 1.584Within Groups 188.29 95 1.982 Total 200.85 99 Group of answer choices0.08220.04510.03550.0228Question 12 2 ptsIf you have a Factorial ANOVA design with two independent variables, you must test to see if your first IV is significant, if your 2nd IV is significant, and whether an interaction of the two IV's is significant. Group of answer choicesTrueFalseQuestion 13 2 ptsWhich of the following is an example of a simple effect analysis in a Factorial ANOVA?Group of answer choicesThere are significant differences across all groups of the 1st IV.There are significant differences across all levels of the 1st IV, but only for one level of the 2nd IV,There are significant differences across all combinations of groups from both IV1 and IV2.In the 1st IV, group 1 is significantly different than group 2, but group 1 is not significantly different than group 3.Question 14 4 ptsCalculate a Tukey HSD value for a one-way ANOVA (based on the following information)...qT = 4.201 MS (within) = 21.88 n = 15Group of answer choices6.1286.86576.115.5355.07Question 15 2 ptsGiven the following group means from a 2 x 2 Factorial ANOVA: Variable A Group 1 Group 2 Variable B Group 1 20 40Group 2 20 40Which variables (if any) show a main effect?Group of answer choicesThere is a main effect of both Variable A and Variable B.There is no main effect for either Variable A or Variable B.There is a main effect of Variable B only.There is a main effect of Variable A only.Question 16 2 ptsIf you have designed a research study with 1 categorical IV (which is split into three separate groups) and 1 ratio DV, you should use a one-way ANOVA to determine if there are any significant differences across all of the groups. Group of answer choicesTrueFalseQuestion 17 2 ptsIn a one-way ANOVA, the three main factors that influence Within Group error are:1. How close the group means are to each other2. How spread out the variances of the groups are3. Whether your IV is a categorical vs. ordinal variableGroup of answer choicesTrueFalseQuestion 18 2 ptsPost-hoc tests are conducted ...Group of answer choicesAfter a one-way ANOVA, to see if the overall one-way ANOVA was significant or not.After a one-way ANOVA, to see which groups are significantly different from each other.Before a one-way ANOVA is conducted, to see which groups are significantly different from each other firstWhen we want to see how influential the IV is in changing the DV.