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The graph of the function fon the interval 0 s x s 9 consists of three line segments and the point (4, 4), as shown. It is given that 1599"" ; .5 and J:g(x)dx :12. -4- 0 {11012345678910 Part A: Find the value of J': ")0de or explain why the integral does not exist. (3 points) Part 8: Find the value of ngumx Show the work that leads to your answer. (3 points) Part c: Find the value of 1:99")- f(x)]dx_ Show the work that leads to your answer. (4 points) A continuously-decreasing function that is concave down on the interval [3,7] is represented by the table. x 3 4.5 5 6.1 7 f(x) 1.946 1.705 1.609 1.361 1.099 Part A: Find the left Reimann sum estimate of I: and," based on the subintervals given in the table. (4 points) Part B: Write the midpoint Reimann sum that estimates J: f(x)dxl based on the subintervals given in the table. (4 points) Part C: Determine whether the left Reimann sum estimate is an overestimate or an underestimate, based on the properties of the function. (2 points) Let fbe a twice-differentiable function with derivative given by f'(x) = -4x3 + 12x2. Part A: Find the x-coordinate of any possible critical points of f. Show your work. (2 points) Part B: Find the x-coordinate of any possible inection points of f. Show your work. (2 points) Part C: Use the Second Derivative Test to determine any relative extrema and inection points. Justify your answers. (3 points) Part D: If f has only one critical point on the interval [2, 4], what is true about the function fon the interval [2,4]? Justify your answers. (3 points) Part A: Complete the table with positive, negative, or 0 to describe 9' and g". Justify your answers. (3 points) x 3