3. Find local extrema of f (x) = 0.6x3 - 4x3 + 1 , and then absolute extrema over [-2.5, 3] by the 2-nd derivative test. At what x the 2-nd derivative test is inconclusive? Summary of the Answer: at X = the second derivative test is inconclusive; at x = the function f (x) achieves its local max / min (circle the correct one) , which is at X = the function f (x) achieves its local max / min (circle the correct one) , which is at X = the function f (x) achieves its absolute max / min (circle the correct one), which is at X = the function f (x) achieves its absolute max / min (circle the correct one), which is 4. ( 10 points) The figure on the right is the graph of a function 2 f (x). What is the value of the definite integral S_ f (x) dx 8 5. ( 10 points each) Evaluate the definite integral: "(5 cost + 2 sec2 t ) dt6. The graph shows the position function of a car in miles at time t hours. We have learned that the derivative of the position function is the velocity function. Use the shape of the graph to explain your answers to the following questions. position of car in miles 2 2 3 5 6 time in hours a. Was the car going faster at point A or point B? Provide a brief explanation. b. What happened between points C and D? Provide a brief explanation. C. What is the velocity of the car at point E? Describe the motion of the car around point E. Provide a brief explanation.12x (Dc-132 and specify the points of local extrema showing application of the first derivative test. 1. Find the intervals on which the graph of f(x) = is increasing or decreasing Summary of the Answer: function f(x) increases at function f(x) decreases at at x = the function f(x) achieves its local max/ min (circle the correct one), which is 2. Find inflection points of f(x) = 0.63:5 4x3 + 1 and specify intervals of concavity. Summary of the Answer: function f(x) is concave upward at ; function f(x) is concave downward at ; the points of inflection of at) are at x = where the function is equal