(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
5kmaway from the intersection and is moving at
1.2k(m)/(m)in. At the same time, car
Bis
8kmfrom 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)
