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)