Use the derivative f'(x) = x (x-5)(x + 1) to determine the local maxima and minima off and the intervals of increase and decrease. Sketch a possible graph of f (f is not unique) The local maximum/maxima is/are at x= (Use a comma to separate answers as needed.] The local minimum/minima is/ara at x=] (Use a comma to separate answers as needed.) The interval(s) of increase is'are (Type your answer in interval notation Use a comma to separate answers as needed ) The interval(s) of decrease is(are) (Type your answer in interval notation. Use a comma to separate answers as needed.) Which is a possible graph of ? O A. O B. OC. O D. O OWhat point on the parabola y =5-x" is closest to the point (5.5)? The point on the parabola y = 5-x that is closest to the point (5,5) is (Type an ordered pair. Round to two decimal places as needed.)Perform a first derivative test on the function fix) = vx Inx (0.co) a. Locate the critical points of the given function. b. Use the First Derivative Test to locate the local maximum and minimum values c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). c. Identify the absolute maximum value of the function. Select the correct choice below and, if necessary, fill in the answer box within your choice O) A. The absolute maximum value is (Type an exact answer in terms of c.) O B. There is no absolute maximum. Identify the absolute minimum value of the function. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The absolute minimum value is (Type an exact answer in terms of e.) O) B. There is no absolute minimum OneDrivePerform a first derivative test on the function fix) = vx Inx (0.co) a. Locate the critical points of the given function. b. Use the First Derivative Test to locate the local maximum and minimum values c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). Locate the local minimum value. Select the correct choice below and, if necessary. fill in the answer box within your choice O A. There is a local minimum al x = (Type an exact answer in terms of c.) O B. There is no local minimum c. Identify the absolute maximum value of the function. Select the correct choice below and, if necessary, fill in the answer box within your choice A. The absolute maximum value is (Type an exact answer in terms of c.) O B. There is no absolute maximum. Identify the absolute minimum value of the function. Select the correct choice below and, if necessary, fill in the answer box within your choice.The volume of a cube decreases at a rate of 0.5 n / min. What is the rate : length when the side lengths are 7 17 f- / min. se Write an equation relating the volume of a cube. V. and an edge of the cut f / min. Differentiate both sides of the equation with respect to t it/ min. se dV dt (Type an expression using s as the variable.) SC The rate of change of the side longth when the side langths are 7 it is (Type an integer or a decimal. Round to five decimal places as needed.) seA rope passing through a capstan on a dock is attached to a boat offshore. The rope is pulled in at a constant rate of 3 ft /s, and the capstan is 4 it vertically above the water. How fast is the boat traveling when it is 5 it from the Let x be the horizontal distance from the boat to the dock and he rope. Write an equation relating x and z Differentiate both sides of the equation with respect to t. dx zp When the boat is 5 ft from the dock, it is traveling at about (Round to two decimal places as needed.)A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y = 36-x". What are the dimensions of the rectangle with the maximum area? What is the area? In the rectangle with the maximum area, the shorter dimension is about and the longer dimension is about (Round to two decimal places as needed.) The maximum area of the rectangle is about (Round to two decimal places as needed.)