1. The rate of change of y with respect to x is 13.

2. The rate of change of volume with respect to time is 3 m^{3} / minute.

3. a. The rate of change of y with respect to x is 4.

b. x = 9

4. The maximum area of the rectangle is 576 cm^{2.}

5. The minimum value of x^{2} + y^{2} is 72.

6. Maximum area that can be fenced is 45 000 m^{2.}

7.

a. Length = 90 − 2x

b. Width = 60 − 2x

c. V = (90 − 2x)(60 − 2x)x = 5400x − 300x^{2}+ 4x^{3}d. The maximum volume of the box is 28520 cm^{2}

8.

a.Acceleration = 6t − 4

b. Initial acceleration is -4 m/s^{2}c. s = t^{3}− 2t^{2}+ 10t

d. Distance is 72 metres

9.

a. Acceleration is -6 m/s

^{2}b. After 6 seconds the ball is at its highest point.

c. The ball will reach the ground again after 12 seconds.

10.

a. s = 2.5t

^{2}− 3t − 13.5

b. s = 34 metres

c. Acceleration is 5 m/s^{2}