Find the relative extrema of the function, if they exist. You must justify your answer using the first -derivative test. 1) f(x) = x4 - 18x2 + 4

Find the relative extrema of the function and classify each as a maximum or minimum. You must justify your answer using the second-derivative test. Q2 f(x) = x2(5 - x)2

Find the points of inflection. Q3. f(x) = 9x / x2 + 25

Determine where the given function is concave up and where it is concave down. Q4 f(x) = (x + 3)2/3 - 6

Q5

27 5) P(x) = -x3 + ?x2 - 60x + 100, x 2 5 is an approximation to the total profit (in thousands of dollars) from the sale of x hundred thousand tires. Find the number of tires that must be sold to maximize profit. 6) An appliance company determines that in order to sell x dishwashers, the price per dishwasher must be It also determines that the total cost of producing x dishwashers is given by C(x) = 3000 + 0&2. How many dishwashers must the company produce and sell in order to maximize profit? Use the differential to find a decimal approximation of the radical expression. Round to four decimal places. Points: 3 3 7) ~34Differentiate implicitly to find the slope of the curve at the given point. Points: 3 8) x3y3 = 8,- (2, 1) Solve the problem. Points: 4 9) Given the revenue and cost functions R(x) = 24x - 0.3x2 and C(x) = 6x + 15, where x is the daily production, find the rate of change of prot with respect to time when x = 15 units and % = 5 units per day. Points: 4 10) The radius of a right circular cylinder is increasing at the rate of 8 in./s, while the height is decreasing at the rate of 4 in.,"s. At what rate is the volume of the cylinder changing when the radius is 8 in. and the height is 12 in.? Provide an exact answer only no decimal approximations