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).
ii) Find when the velocity is zero
iii) Find the greatest height reached by the ball.
iv) What is the acceleration of the ball at any time?
Thanks a million!