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(10) 1. Suppose f(x)=

3

x+2

. Use the denition of derivative to nd f

0

(x).

(9) 2. Find an equation for the line tangent to the graph of y=

4x

2+x

2

at the point where

x=1.

(12) 3. Assume that the functions u(x) and v(x) are dened and dierentiable for all real

numbers x. The following data is known about u,v, and their derivatives.

x u(x)v(x)u

0

(x)v

0

(x)

2 3 4 1 2

3 2 1 3 1

4 1 3 0 2

Dene f(x) = u(x)v(x), g(x) = u(x)=v(x), and h(x) = u(v(x)). Give the values of the

following with a brief indication of how they were obtained:

a) f

0

(2)

b) g

0

(3)

c) h

0

(4)

(14) 4. Suppose that the function f(x)isdescribed by

f(x)=

8

<

:

3x

2

if x<0

Ax +Bif 0 x1

2

x

if 1 <x

:

a) Find Aand Bso that f(x)iscontinuous for all numbers. Briey explain your answer.

b) Sketch y=f(x) on the axes given for the values of Aand Bfound in a) when xis in

the interval [2;2].

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