A particle moves according to the law of motion
\(s = t ^ { 3 } - 7 t ^ { 2 } + 5 t , \quad t \geq 0\)
where \( t \) is measured in seconds and \( s \) in feet.
a.) Find the velocity at time \( t \) . Answer:
b.) What is the velocity after \( 3 \) seconds? Answer:
c.) When is the particle at rest? Enter your answer as a comma separated list. Enter None if the parcicle is never at rest. Answer:
d.) When is the particle moving in the positive direction?
When \( 0 \leq t < \) ___and \(t> \)___
\(a)3t^2- 14t+ 5\\b)- 10\\c)4.27698 ,0.38968\\d)0.38968,4.27698\)
If \( y = f ( g ( h ( x ) ) ) , \) then the derivative \( y ^ { \prime } \) is given by which for
a) \( f ^ { \prime } ( g ( h ( x ) ) \)
b) \( f ^ { \prime } ( g ( h ( x ) ) h ^ { \prime } ( x ) \)
c) None of these
d) \( f ^ { \prime } ( g ( h ( x ) ) g ^ { \prime } ( h ( x ) ) \)
e) \( f ^ { \prime } ( g ( h ( x ) ) g ^ { \prime } ( h ( x ) ) h ^ { \prime } ( x )\)
Determine the following limits. If infinite, specify \( \infty \) or \( - \infty \) . If an answer does not exist, explain why. (NO POINTS WILL BE GIVEN IF A TABLE OF VALUES IS USED) b. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
