Spring 2006

Show all work in a neat and organized fashion. Clearly indicate your answers.

20 points possible.

1. (4 pts.) Submit your GSP take-home problem.

2. (8 pts.) Differentiate. Simplify as much as possible.

(a)

f(x)= x3+2x-5 Öx

(b)

G(s)=(s3+3)(s7+2s)

3. (3 pts.) Suppose h(x)=x²g(x), where g(7)=9 and g¢(7)=11. Find h¢(7).

4. (5 pts.) A particle moves according to a law of motion s=f(t), t ³ 0, where t is measured in seconds and s in feet.

f(t)=t3-15t2+48t

(a) Find the velocity at time t.

(b) What is the velocity after 3 seconds?

(c) When is the particle at rest?

(d) When is the particle moving in the positive direction?