有幾條關於Differentiation問題唔識做(希望有詳細步驟 同教學)?

1. A bullet is fired straight upward from ground with a velocity of 400

m/s from physics, its height h above the ground after t seconds is
h(t)= -16t^2+400t

a. find the time(sec) and the velocity(m/s)

v(t) = h'(t) = 400 - 32t



b. find the maximum height achieved by the bullet

v(t) = 0

=> t = 400/32 = 12.5"

=> max = h(12.5) = 400*12.5 - 16*12.5^2 = 2500 m



c.find the acceleration d^2h/st^2 at any time t.

a(t) = v'(t) = -32 m/s^2





2. A missile is fired into air and h of the missile after t is given by
h(t) = 19.2t - 4.8t^2


b. the velocity at height point

v(t) = h'(t) = 19.2 - 9.6t


a. find initial velocity of the missile

vo = v(0) = 19.2 m/s



c.the heightest location

v(t) = 0

=> t = 19.2/9.6 = 2"

=> max = h(2) = 19.2*2 - 4.8*4 = 19.2 m





3. The daily profit=p, of a residential flat developer is given by

p(x)=800x-2x^2

a. how many flat sold per day will give maximum profit?

p'(x) = 800 - 4x = 0

x = 200 units




b.what is the maximum profit(daily)?

max = p(200)

= 800*200 - 2*40000

= 8000 $

唔好意思...仲有一題

The daily profit, p, of a residential flat developer is given by

p=800x-2x^2

a, how many flat sold per day will give maximum profit?
b, what is the maximum profit(daily)?