So we came back from christmas break and jumped right into studying for midterms, so I don't remember how to do these. I did what I could, but can someone please help?
problems on the top, answers on the bottom
4) Water is draining at the rate of 48π ft^3/min from the vertex at the bottom of a conical tank whose diameter at its base is 40 ft and whose height is 60 ft.
a) find an expression for the volume of water in the tank in terms of its radius at the surface of the water.
b) at what rate is the radius of the water in the tank shrinking when the radius is 16 ft?
c) how fast is the height of the water in the tank dropping at the instant that the radius is 16 ft?
5) Let f be the function given by f(x) = 2x^4 - 4x^2 + 1
a) Find an equation of the line tangent to the graph at (-2, 17)
b) find the x and y coordinates of the relative maxima and relative minima. Verify your answer.
c) Find the x and y coordinates of the points of inflection. verify your answer.
6) Let f(x) = integral from 0 to x of [cos(t/2) + (3/2)]dt on the closed interval [0,4π]
a) Approximate F(2π) using four inscribed rectangles.
b) Find F'(2π)
c) Find the average value of F'(x) on the interval [0,4π]
c) no idea how to go about that
5) a) I know that you use limits.......
b) I know that the critical points are at -1, 0, and 1, but I don't know what to do from there
c) no idea how to go about that.
6) a) 6π
I'm fairly sure that I have 6 mostly wrong, as well as the other two, but at least I tried....can someone please help?