PLEASE SOLVE THIS WORKSHEET AND PLEASE ONLY DO IT HAND WTITTEN WITH BLUE OR BLACK INK PEN PLEASE, REMEMBER I ONLY WANT IT DONE HAND WRITTEN AND WITH BLUE OR BLACK IN PEN, PLEASE WRITE VERY CLEARLY, THANK YOU.

2] Suppose that for a certain twice-differentiable function g , the following are true: 2121 = U - 5'12} = 4.81431 = B. {1-3} = 1\": 515} = D. and 3'15} = E'- a} List the given critical points of g in increasing order: b] List all of the domain values at which g has a local minimum. Justify your answer with a statement about concavlty. If there are no local minimums, then say so. c} List all of the domain values at which E has a local maximum. Justify your answer with a statement about concavity. If there are no lolll maximums, then say so. 3) The graph of the derivative of the function h is given in red . -3 -2 2 3 5 L a) List all the domain values of h at which a local maximum occurs. b) List all the domain values of h at which a local minimum occurs. c) Does h have an inflection point somewhere between x = 3.1 and x = 3.9 ? d) Does h have an inflection point between x = -2.9 and x = -2.1? e) How many inflection points does h have?4) Suppose that the function f is defined by f(x) = 5x3 -10x2-8x + 25, with domain [-2, 6] . a) Calculate the slope of the secant line that connects the two points (-2, f(-2) ) & (6, f(6) ) . This slope is b) Explain how we can be certain that there exists a number k between -2 and 6 such that the first derivative of f evaluated at k equals 92.5) An open-top rectangular tank that has a square base x feet on one side and a height of y feet is to be built with its top flush with the ground to catch runoff water. The material used to make the tank costs 50 dollars per square foot. In addition to the material cost, there is an excavation cost to install the tank below the ground and the excavation cost is 10xy dollars. The volume of the tank must be 1125 cubic feet. a) Draw a diagram of this tank with the dimensions labeled in terms of x and y. b) Construct the equation for the total cost C(x) of this tank. C(x) = c) Find the values of x and y that will minimize the cost. Show your calculation of the derivative of C(x) with respect to x .6) Suppose that the cost (in dollars) to manufacture x items is given by the following function: C(x) = x3 - 0.45x2 + 0.35x + 20000. The revenue for one item is $18,000. a) Find the production level that will maximize the profit. Round your answer to the nearest integer. X = b) Use the answer in part (a) to calculate the maximum profit.T] A certain window is in the shape of a rectangle surmounted hv a semicircle. The rectangular glass is clear [not tinted}. The semicircular glass is tinted and only:I lets in half as much light per unit area as the clear glass. The perimeter is xed at P units. Find the dimensions of the window that will admit the most light. Assume the base of the rectangular glass is 2r inches and the height of the rectangular glass is h inches. See diagram below. Hint: The radius r that maximizes the amount of light will be in terms of P, the perimeter. "'2rF The dimensions that let in the most light are: r= and h