Hey all,

Currently revising for my year 12 maths exam need help with the following 2 problems regarding differentiation. Thanks a bunch.

1) An open cylindrical plastic container is to be designed so that it has a capacity of 2000 cm^3. Find the dimensions of the container if the manufacturer wants the surface area to be minimised.

2) A ball is thrown vertically upward with an initial velocity of 19.6m/s. The displacement (in m) of the ball above the ground is s=-4.9t^2+19.6t, where t is the number of seconds elapsed from the moment that the ball is thrown.

i) Find the initial velocity of the ball as a f(t). Mr F says:

Sub t = 0 into ds/dt.
ii) Find when the velocity is zero Mr F says:

Solve ds/dt = 0.
iii) Find the greatest height reached by the ball. Mr F says:

Sub value of t from ii into s.
iv) What is the acceleration of the ball at any time? Mr F says:

Find the double derivative of s with respect to t.
Thanks a million!