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# application of derivatives

See attached file for full problem description.

1.Boat A is sailing south at 24 km/h while boat B, which is 48 kilometres due south of A, is sailing east at 18km/h.

a)At what rate are they approaching or separating one hour later?
b)When do they cease to approach on another and how far apart are they at this time?
c)What is the significance of the distance in part b)?

2.A rocket is fired into the air and its height in metres at any given time t seconds can be calculated by h(t)=225+49t-0.98t2.

Find the maximum height of the rocket and the time at which it occurs.

3.Find the derivative of the following functions.
2
a)y=2log75x+3-x supposed to be -x2
b)y=(2x3+5)(3x2-x)
2
c)y=x2-7___ * ex supposed to be x2
2x+1

#### Solution Summary

The solution is comprised of detailed explanations of calculation of derivatives of functions. It also explains step-by-step on how to find the maximum height of rocket by the first derivative test.

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