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# (Solved): Given f(x)=sin^(-1)(\sqrt(x^(3)+4)), find f^(')(x) and simplify: (4) A stone is dropped into a lake ...

Given

f(x)=sin^(-1)(\sqrt(x^(3)+4))

, find

f^(')(x)

and simplify: (4) A stone is dropped into a lake, creating a circular ripple that travels outward from where the stone hit the water. The area of the circle enclosed by the ripple is growing at the steady rate of

4f(t^(2))/()

second. a. Find the rate at which the radius of circle is changing when the radius is

1ft

?

2ft

?

5ft

? (5) 2 continued. A stone is dropped into a lake, creating a circular ripple that travels outward from where the stone hit the water. The area of the circle enclosed by the ripple is growing at the steady rate of

4f(t^(2))/()

second. b. Just as the stone is about to hit the water there is no circular ripple. What is the rate of change in the radius when the radius is zero

ft

? Explain the mathematical result. (3) Two cars are traveling away from the same intersection on mutually perpendicular roads. At a certain moment car A is

5km

away from the intersection and is moving at

1.2k(m)/(m)in

. At the same time, car

B

is

8km

from the intersection and is moving at

0.9k(m)/(m)in

. At what rate is the angle

\theta

(see diagram) changing at that instant? (5) For each function, find the critical numbers and classify them as local maximum or local minimum: a.

f(x)=x^(3)-x^(2)+x

. Also, find the inflection point. (5) b.

g(t)=4t-tant

. (5)

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