1) Find the derivative of the function. g ( w ) = 6 2)A rocket can rise to a hei

Question

1) Find the derivative of the function.

g(w) = 6

2)A rocket can rise to a height of

h(t) = t3 + 0.1t2

feet in t seconds. Find its velocity and acceleration 12 seconds after it is launched.

3)ountry Motorbikes Incorporated finds that it costs $200 to produce each motorbike, and that fixed costs are $1300 per day. The price function is

p(x) = 600 5x,

where p is the price (in dollars) at which exactly x motorbikes will be sold. Find the quantity Country Motorbikes should produce and the price it should charge to maximize profit. Also find the maximum profit.

Explanation / Answer

In Q-1, function g(w) is not clearly given so I'm doing Q-2.In Q-2 I am also doing derivative for calculating velocity and acceleration.By using this method you can also do Q-1.

2) h(t) = t3 + 0.1 t2

V(velocity) = dh / dt

V = d/dt ( t3 + 0.1 t2 )

V = 3 t2 + 0.1*2 t

V = 3 t2 + 0.2 t

V( at t=12 sec) = 3(12)2 + 0.2*12

= 434.4 ft/s

----------------------------------------

a (acceleration) = dV/ dt

a = d/dt(  3 t2 + 0.2 t )

a = 3*2 *t + 0.2

a= 6 t + 0.2

a( at t= 12 s) = 6*12 + 0.2 = 72.2 ft/s2

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