MTH 151

Quiz 3

Fall 2011

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

20 points possible.

1. (9 pts.) Differentiate each function. You do not have to simplify your answers.

(a)

y= 1+3x x5−x2

(b)

H(x)=cosx+sinx+secx

(c)

w(θ)=tan3θ

2. (3 pts.) If f(x)=√x g(x), where g(4)=12 and g′(4)=11, find f′(4).

3. (3 pts.) Find dy/dx by implicit differentiation.

x2+xy−y2=16

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

f(t)=2t3−30t2+50t

(a) What is the velocity after 2 seconds?

(b) When t=2, is the particle moving in the positive direction, the negative direction, or neither?

(c) When t=2, is the particle speeding up, slowing down, or neither?

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