Elective Mathematics

1The volume of a cube of side x is changing. dV/dx when x = 3 is

2The radius of a circle increases at 2 cm/s. How fast is its area increasing when r = 5 cm?

3An open box is made from a 12 cm square sheet by cutting squares of side x from each corner. The value of x that maximises volume is

4The equation of the tangent to y = x² at (1, 1) is

5If s = t³ − 3t, the velocity at t = 2 is

6A rectangle has perimeter 40 cm. Its maximum possible area is

7At what value of x does y = x² − 6x + 5 have a stationary point?

8A particle moves so that s = t³ − 2t. Find its velocity at t = 2.

9A stationary point is a maximum if d²y/dx² is

10If y = x³, find the rate of change of y when x = 2.