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 m3 / 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 cm2.

5. The minimum value of x2 + y2 is 72.

6. Maximum area that can be fenced is 45 000 m2.

7.

a. Length = 90 − 2x
b. Width = 60 − 2x
c. V = (90 − 2x)(60 − 2x)x = 5400x − 300x2 + 4x3
d. The maximum volume of the box is 28520 cm2

8.

a.Acceleration = 6t − 4
b. Initial acceleration is -4 m/s2
c. s = t3 − 2t2 + 10t
d. Distance is 72 metres

9.

a. Acceleration is -6 m/s2
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 = 2.5t2 − 3t − 13.5
b. s = 34 metres
c. Acceleration is 5 m/s2