1) A cylindrical tank full of water measures

1)A cylindrical tank full of water measures 3 feet high and has a circular base with a radius of 1 foot. Suppose the tank is drained at a rate of ¼ cubic foot per minute. What is the rate of change in the height of the water in the tank with respect to time?2)A spherical weather balloon is filled with helium such that its radius is growing at a constant rate of 2 feet per minute. Assuming V = volume of the balloon = 4π/3 * r^(3), where r = radius of the balloon, what is the rate of change in the volume of the balloon with respect to time at the moment it has a radius of 3 feet3)Consider f(x) = x^(3/2)-x^(5/2) for x on [0,1]a) At what value of x does f obtain an absolute maximum value on the given interval?b) At what value of x does f obtain an absolute minimum value on the given interval? Express your answers in terms of exact values. No rounded decimal solutions. 4)Use the following function:F(x) = x * e^(x)a) On what interval(s) of x is function f increasing?b) On what interval(s) of x is function f decreasing?c) On what interval(s) of x is function f concave upd) On what interval(s) of x is function f concave downExpress your answers in exact values. No rounded decimals5)Consider f(x) = (3x)/(x^(2)+3) where f’(x) = (3(3-x^(2))/((x^(2)+3)^(2)) and f’’(x) = (6x(x^(2)-9))/((x^(2)+3)^(3)). Sketch a graph of f, include in your sketch the location of key features such as intercept, extrema, inflection points, and asymptotes. 6)Consider f(x) = x^(4) – 9x^(2) Sketch a graph of f, include in your sketch the location of key features such as intercepts, extrema, inflection points, and asymptotes.7)Find the xy coordinate on the graph of y = SQRT(x), nearest the point ( 4,0 ) in the xy coordinate planeNot L is the distance between the point (x,y) and (4,0), where L is calculated using the distance formula as follows,L = L(x,y) = SQRT(((x-4)^2)+((y-0)^(2)))8)On any given day, the flow rate, F (Measured in cars per hour ), on a congested roadway is a function of speed of traffic on the roadway, v ( measured in miles per hour ) For any given v,F(v) = (v)/(46+0.02v^(2))What speed will maximize the flow rate on the road?