Major Calculus Assignment Issue

I know I put one of the questions up earlier, but it would really help me out if someone could give me some input on the rest of these.

1. (a) Determine the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of length 5 cm and 12 cm. The two sides of the rectangle lie along the legs.

(b) Repeat part (a) with a right triangle that has sides 8 cm by 15 cm.

(c) Hypothesize a conclusion for any right triangle.

2. Determine the dimensions of the cone of maximum volume that can be inscribed in a sphere with radius 3?

3. The position, *s*, of an object moving in a straight line from a fixed point at *t* seconds is given by

*s(t)*=*t*^3 - 9*t*^2 - 21*t* - 11, where *t*>0 and *s(t)* is measured in metres.

(a) Determine when the object is stopped and when it is moving forward.

(b) Is the acceleration negative at any time?

(c) When is the object speeding up and when is the object slowing down? Explain why.

Any help would do wonders.