Question 4. (4 points for each part (a)(c), graded for correctness) A witch wants to feed her giant some ice cream. She has a cube of ice cream that has dimensions 1 meter by 1 meter by 1 meter, but she knows the giant will want a 2 meter by 2 meter by 2 meter cube of ice cream. Fortunately, the witch knows an enlarging spell. She casts the enlarging spell which causes all three of the dimensions of the cube of ice cream to increase at a constant rate of 1 meter per second for 1 second after which the the cube of ice cream stays the same. Let V(t) be the volume of the cube of ice cream at time t, where t = 0 is the moment the witch casts the spell. (a) Express V(t) as a piecewisedened function on [1, 2]. Assume the ice cream has not changed for at least one second before the spell is cast and does not change for at least one second after the spell ends