4 Hard Questions!! Help Please!!

Can you please show work? You do not need to answer all the problems even if you know just one your help is appreciated :D

1) A storage tank in the shape of a right circular cone has a height of 6 meters and a base of radius 2 meters. The cone is inverted and fluid is pumped in at a rate of .002m^3-minute (2 liters/min). At what rate is the level of the fluid rising when the tank is filled to a height of 3meters? Use V= (pie X r squared X h)/3 and R = (H)/3

2) Verify the mean-value theorem for

a) f(x) = x^3 - 3x^2 - 13x + 15 on (-3,1)

(b) f(x) = cos 2x - 2 cos^2 x on ((-pie/2),(pie/4))

3) Locate and classify all critical points, points of inflection, intervals where the Function increases/decreases and where the Function is concave up/down for

a) f(x) = x^4 - 4x^2 + 4x^3 + 1

b) f(x) = (1+ squareroot(x) + cuberoot(x))^9

c) f(x) = x/(ln x)^2

d) f(x) = e^x + e^-2x

e) f(x) = e^(x^3 - x)

4) Using differentials, approximate the numerical value of

a) cuberoot(130)

b) ln (3), you know ln (e) = 1

c) log (8), you know log (10) = 1