1.Consider the functionf(x)=12x^5+ 75x^4 -120x^3 +3

f(x)has inflection points at (reading from left to right)x=D,E, andF

where D is

and E is

and F is

For each of the following intervals, tell whether f(x) is concave up or concave down

(- ,D):

(D, E):

(E,F):

(F,):

2.A piece of cardboard measuring 8 inches by 12 inches is formed into an open-top box by cutting squares with side lengthx from each corner and folding up the sides.

Find a formula for the volume of the box in terms ofx

V(x)=

Find the value for x that will maximize the volume of the box

x=

3.A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the radius is 17cm. (Enter a positive value)

The volume is decreasing at a rate of: cm^3/min

4.Find the slope of the tangent line to the curve

4x^2 -2xy -2y^3 =24

at the point (1, -2)